MinT - Best Known (234−139, 234, s)-Nets in Base 4

Best Known (234−139, 234, s)-Nets in Base 4

(234−139, 234, 104)-Net over F₄ — Constructive and digital

Digital (95, 234, 104)-net over F₄, using

t-expansion [i] based on digital (73, 234, 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]

(234−139, 234, 144)-Net over F₄ — Digital

Digital (95, 234, 144)-net over F₄, using

t-expansion [i] based on digital (91, 234, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(234−139, 234, 898)-Net in Base 4 — Upper bound on s

There is no (95, 234, 899)-net in base 4, because

1 times m-reduction [i] would yield (95, 233, 899)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 593564 452119 114641 236060 259376 922142 078567 296605 588696 676052 486325 102728 054378 692848 482215 641299 578518 430698 603016 921959 579736 502957 041344 > 4²³³ [i]