MinT - Best Known (73, 73+91, s)-Nets in Base 4

Best Known (73, 73+91, s)-Nets in Base 4

(73, 73+91, 104)-Net over F₄ — Constructive and digital

Digital (73, 164, 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]

(73, 73+91, 112)-Net over F₄ — Digital

Digital (73, 164, 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]

(73, 73+91, 854)-Net in Base 4 — Upper bound on s

There is no (73, 164, 855)-net in base 4, because

1 times m-reduction [i] would yield (73, 163, 855)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 140 104051 811532 718766 242024 129125 120304 163369 149912 418313 790740 468699 738733 976804 772395 591108 717416 > 4¹⁶³ [i]