MinT - Best Known (178−104, 178, s)-Nets in Base 4

Best Known (178−104, 178, s)-Nets in Base 4

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

Digital (74, 178, 104)-net over F₄, using

t-expansion [i] based on 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]

(178−104, 178, 112)-Net over F₄ — Digital

Digital (74, 178, 112)-net over F₄, using

t-expansion [i] based on 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]

(178−104, 178, 733)-Net in Base 4 — Upper bound on s

There is no (74, 178, 734)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 149672 797212 721501 699389 124724 364757 256249 567982 838870 991725 465226 193305 506608 856803 017199 428665 717660 931110 > 4¹⁷⁸ [i]