MinT - Best Known (255−155, 255, s)-Nets in Base 4

Best Known (255−155, 255, s)-Nets in Base 4

(255−155, 255, 104)-Net over F₄ — Constructive and digital

Digital (100, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 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]

(255−155, 255, 144)-Net over F₄ — Digital

Digital (100, 255, 144)-net over F₄, using

t-expansion [i] based on digital (91, 255, 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]

(255−155, 255, 889)-Net in Base 4 — Upper bound on s

There is no (100, 255, 890)-net in base 4, because

1 times m-reduction [i] would yield (100, 254, 890)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 860 778451 418103 664914 460186 681721 229923 618118 106004 275353 028721 543238 941034 865450 898531 108891 997697 019143 870801 837536 648367 141985 024551 383848 244845 102164 > 4²⁵⁴ [i]