MinT - Best Known (74, 74+111, s)-Nets in Base 4

Best Known (74, 74+111, s)-Nets in Base 4

(74, 74+111, 104)-Net over F₄ — Constructive and digital

Digital (74, 185, 104)-net over F₄, using

t-expansion [i] based on digital (73, 185, 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]

(74, 74+111, 112)-Net over F₄ — Digital

Digital (74, 185, 112)-net over F₄, using

t-expansion [i] based on digital (73, 185, 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]

(74, 74+111, 690)-Net in Base 4 — Upper bound on s

There is no (74, 185, 691)-net in base 4, because

1 times m-reduction [i] would yield (74, 184, 691)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 621 562878 866762 438744 442048 360472 780041 336395 458411 287455 893545 431704 788690 003213 360661 303684 491540 157085 703424 > 4¹⁸⁴ [i]