MinT - Best Known (94−59, 94, s)-Nets in Base 4

Best Known (94−59, 94, s)-Nets in Base 4

(94−59, 94, 56)-Net over F₄ — Constructive and digital

Digital (35, 94, 56)-net over F₄, using

t-expansion [i] based on digital (33, 94, 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]

(94−59, 94, 65)-Net over F₄ — Digital

Digital (35, 94, 65)-net over F₄, using

t-expansion [i] based on digital (33, 94, 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]

(94−59, 94, 299)-Net in Base 4 — Upper bound on s

There is no (35, 94, 300)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁹⁴, 300, S₄, 59), but
- the linear programming bound shows that MÂ â‰¥ 186258 380978 443120 781754 241176 171953 190384 693181 137894 803388 708045 305292 237442 677451 395547 205501 953538 155565 253919 178565 467076 673302 754888 777728 / 301 833638 810559 566235 575477 656446 845272 582882 172810 391590 643908 779438 066505 655636 879877 > 4⁹⁴ [i]