MinT - Best Known (75, 177, s)-Nets in Base 4

Best Known (75, 177, s)-Nets in Base 4

(75, 177, 104)-Net over F₄ — Constructive and digital

Digital (75, 177, 104)-net over F₄, using

t-expansion [i] based on digital (73, 177, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(75, 177, 112)-Net over F₄ — Digital

Digital (75, 177, 112)-net over F₄, using

t-expansion [i] based on digital (73, 177, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(75, 177, 772)-Net in Base 4 — Upper bound on s

There is no (75, 177, 773)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38872 123372 215110 571704 658074 972159 730840 130622 922330 967327 765136 148134 717927 841583 612603 510285 225329 737920 > 4¹⁷⁷ [i]