MinT - Best Known (73, 178, s)-Nets in Base 4

Best Known (73, 178, s)-Nets in Base 4

(73, 178, 104)-Net over F₄ — Constructive and digital

Digital (73, 178, 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, 178, 112)-Net over F₄ — Digital

Digital (73, 178, 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, 178, 713)-Net in Base 4 — Upper bound on s

There is no (73, 178, 714)-net in base 4, because

1 times m-reduction [i] would yield (73, 177, 714)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38437 598298 900452 860391 151527 610523 827095 047162 062172 453704 520046 899709 704503 311465 366413 143807 053708 721400 > 4¹⁷⁷ [i]