MinT - Best Known (59−27, 59, s)-Nets in Base 4

Best Known (59−27, 59, s)-Nets in Base 4

(59−27, 59, 66)-Net over F₄ — Constructive and digital

Digital (32, 59, 66)-net over F₄, using

1 times m-reduction [i] based on digital (32, 60, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 30, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]

(59−27, 59, 72)-Net over F₄ — Digital

Digital (32, 59, 72)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(59−27, 59, 906)-Net in Base 4 — Upper bound on s

There is no (32, 59, 907)-net in base 4, because

1 times m-reduction [i] would yield (32, 58, 907)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 83343 403237 399578 733290 999547 455040 > 4⁵⁸ [i]