MinT - Best Known (96, 257, s)-Nets in Base 4

Best Known (96, 257, s)-Nets in Base 4

(96, 257, 104)-Net over F₄ — Constructive and digital

Digital (96, 257, 104)-net over F₄, using

t-expansion [i] based on digital (73, 257, 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]

(96, 257, 144)-Net over F₄ — Digital

Digital (96, 257, 144)-net over F₄, using

t-expansion [i] based on digital (91, 257, 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]

(96, 257, 796)-Net in Base 4 — Upper bound on s

There is no (96, 257, 797)-net in base 4, because

1 times m-reduction [i] would yield (96, 256, 797)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13410 519671 658586 556998 237835 842384 947767 344619 001752 124610 770635 611018 418968 891826 946091 455271 971600 039281 976696 415580 450403 378299 384818 765686 793835 757868 > 4²⁵⁶ [i]