MinT - Best Known (58−36, 58, s)-Nets in Base 4

Best Known (58−36, 58, s)-Nets in Base 4

(58−36, 58, 34)-Net over F₄ — Constructive and digital

Digital (22, 58, 34)-net over F₄, using

t-expansion [i] based on digital (21, 58, 34)-net over F₄, using
- net from sequence [i] based on digital (21, 33)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
    - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(58−36, 58, 44)-Net over F₄ — Digital

Digital (22, 58, 44)-net over F₄, using

t-expansion [i] based on digital (21, 58, 44)-net over F₄, using
- net from sequence [i] based on digital (21, 43)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 44, using
    - a curve from the manYPoints database [i]

(58−36, 58, 205)-Net in Base 4 — Upper bound on s

There is no (22, 58, 206)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 89224 717124 925141 872046 674245 827112 > 4⁵⁸ [i]