MinT - Best Known (125−59, 125, s)-Nets in Base 4

Best Known (125−59, 125, s)-Nets in Base 4

(125−59, 125, 76)-Net over F₄ — Constructive and digital

Digital (66, 125, 76)-net over F₄, using

1 times m-reduction [i] based on digital (66, 126, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 63, 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]

(125−59, 125, 115)-Net over F₄ — Digital

Digital (66, 125, 115)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−59, 125, 1436)-Net in Base 4 — Upper bound on s

There is no (66, 125, 1437)-net in base 4, because

1 times m-reduction [i] would yield (66, 124, 1437)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 457 824258 313672 860558 709466 596780 651720 014466 550009 663011 902092 235845 131540 > 4¹²⁴ [i]