MinT - Best Known (246−129, 246, s)-Nets in Base 4

Best Known (246−129, 246, s)-Nets in Base 4

(246−129, 246, 130)-Net over F₄ — Constructive and digital

Digital (117, 246, 130)-net over F₄, using

t-expansion [i] based on digital (105, 246, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(246−129, 246, 168)-Net over F₄ — Digital

Digital (117, 246, 168)-net over F₄, using

t-expansion [i] based on digital (115, 246, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(246−129, 246, 1606)-Net in Base 4 — Upper bound on s

There is no (117, 246, 1607)-net in base 4, because

1 times m-reduction [i] would yield (117, 245, 1607)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3205 423499 909389 093143 921587 514478 278455 107569 870372 088234 879207 454947 871223 773721 618723 052156 408314 917392 600535 238452 087911 806245 359621 334106 944665 > 4²⁴⁵ [i]