MinT - Best Known (188−115, 188, s)-Nets in Base 4

Best Known (188−115, 188, s)-Nets in Base 4

(188−115, 188, 104)-Net over F₄ — Constructive and digital

Digital (73, 188, 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]

(188−115, 188, 112)-Net over F₄ — Digital

Digital (73, 188, 112)-net over F₄, using

net from sequence [i] based on digital (73, 111)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
  - Drinfeld modules of rank 1 [i]

(188−115, 188, 649)-Net in Base 4 — Upper bound on s

There is no (73, 188, 650)-net in base 4, because

1 times m-reduction [i] would yield (73, 187, 650)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 40811 424063 803975 852920 228755 458130 705877 886677 881239 187280 156103 108483 537773 397994 284430 514900 405822 834763 243656 > 4¹⁸⁷ [i]