MinT - Best Known (128−93, 128, s)-Nets in Base 4

Best Known (128−93, 128, s)-Nets in Base 4

(128−93, 128, 56)-Net over F₄ — Constructive and digital

Digital (35, 128, 56)-net over F₄, using

t-expansion [i] based on digital (33, 128, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(128−93, 128, 65)-Net over F₄ — Digital

Digital (35, 128, 65)-net over F₄, using

t-expansion [i] based on digital (33, 128, 65)-net over F₄, using
- net from sequence [i] based on digital (33, 64)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(128−93, 128, 145)-Net in Base 4 — Upper bound on s

There is no (35, 128, 146)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4¹²⁸, 146, S₄, 93), but
- the linear programming bound shows that MÂ â‰¥ 278138 826057 886185 243354 511782 966260 650098 300721 458938 504666 442284 028621 359345 744239 132672 / 1 630392 203869 > 4¹²⁸ [i]