MinT - Best Known (94, 227, s)-Nets in Base 4

Best Known (94, 227, s)-Nets in Base 4

(94, 227, 104)-Net over F₄ — Constructive and digital

Digital (94, 227, 104)-net over F₄, using

t-expansion [i] based on digital (73, 227, 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]

(94, 227, 144)-Net over F₄ — Digital

Digital (94, 227, 144)-net over F₄, using

t-expansion [i] based on digital (91, 227, 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]

(94, 227, 922)-Net in Base 4 — Upper bound on s

There is no (94, 227, 923)-net in base 4, because

1 times m-reduction [i] would yield (94, 226, 923)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11714 524857 156609 303849 637638 943557 350795 657930 347944 433142 279818 828882 596677 572601 119893 501634 649089 951097 014649 767367 722377 962459 779450 > 4²²⁶ [i]