The 30 lines of the affine plane certainly can be broken to 6 rounds or parallel lines.
(
ABCDE FGHIJ KLMNO PQRST UVWXY
AFKPU AGMSY AHOQX AILTW AJNRV
BFOSW BGLQV BHNTU BIKRY BJMPX
CFNQY CGKTX CHMRW CIOPV CJLSU
DFMTV DGORU DHLPY DINSX DJKQW
EFLRX EGNPW EHKSV EIMQU EJOTY
)
Update: yeah, the example is wrong, but the statement is still true. Uh.
ABCDE FGHIJ KLMNO PQRST UVWXY
AFKPU BGLQV CHMRW DINSX EJOTY
AGMSY BHNTU CIOPV DJKQW EFLRX
AHOQX BIKRY CJLSU DFMTV EGNPW
AILTW BJMPX CFNQY DGORU EHKSV
AJNRV BFOSW CGKTX DHLPY EIMQU
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