MinT - Best Known (226−133, 226, s)-Nets in Base 4

Best Known (226−133, 226, s)-Nets in Base 4

(226−133, 226, 104)-Net over F₄ — Constructive and digital

Digital (93, 226, 104)-net over F₄, using

t-expansion [i] based on digital (73, 226, 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]

(226−133, 226, 144)-Net over F₄ — Digital

Digital (93, 226, 144)-net over F₄, using

t-expansion [i] based on digital (91, 226, 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]

(226−133, 226, 902)-Net in Base 4 — Upper bound on s

There is no (93, 226, 903)-net in base 4, because

1 times m-reduction [i] would yield (93, 225, 903)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2983 995253 613081 447177 057215 440638 953898 813440 019062 733787 232370 762684 493437 270723 137899 108082 817628 375295 057434 287206 786222 859345 543350 > 4²²⁵ [i]