MinT - Best Known (58−26, 58, s)-Nets in Base 4

Best Known (58−26, 58, s)-Nets in Base 4

(58−26, 58, 76)-Net over F₄ — Constructive and digital

Digital (32, 58, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 29, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(58−26, 58, 906)-Net in Base 4 — Upper bound on s

There is no (32, 58, 907)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 83343 403237 399578 733290 999547 455040 > 4⁵⁸ [i]