MinT - Best Known (94, 94+153, s)-Nets in Base 4

Best Known (94, 94+153, s)-Nets in Base 4

(94, 94+153, 104)-Net over F₄ — Constructive and digital

Digital (94, 247, 104)-net over F₄, using

t-expansion [i] based on digital (73, 247, 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, 94+153, 144)-Net over F₄ — Digital

Digital (94, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 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, 94+153, 801)-Net in Base 4 — Upper bound on s

There is no (94, 247, 802)-net in base 4, because

1 times m-reduction [i] would yield (94, 246, 802)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13441 220904 524504 603743 120182 357302 266735 477098 539381 218006 290483 494072 067851 333676 331774 404228 598668 365134 574531 210095 251254 514722 974346 357393 218720 > 4²⁴⁶ [i]