MinT - Best Known (96, 96+141, s)-Nets in Base 4

Best Known (96, 96+141, s)-Nets in Base 4

(96, 96+141, 104)-Net over F₄ — Constructive and digital

Digital (96, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 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, 96+141, 144)-Net over F₄ — Digital

Digital (96, 237, 144)-net over F₄, using

t-expansion [i] based on digital (91, 237, 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, 96+141, 903)-Net in Base 4 — Upper bound on s

There is no (96, 237, 904)-net in base 4, because

1 times m-reduction [i] would yield (96, 236, 904)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12483 065628 256102 740924 323268 772650 016066 349841 104010 117098 902309 212646 127504 885184 828153 999687 704812 278181 329671 591138 712065 599379 489302 859830 > 4²³⁶ [i]