MinT - Best Known (51−23, 51, s)-Nets in Base 4

Best Known (51−23, 51, s)-Nets in Base 4

(51−23, 51, 66)-Net over F₄ — Constructive and digital

Digital (28, 51, 66)-net over F₄, using

1 times m-reduction [i] based on digital (28, 52, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 26, 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]

(51−23, 51, 68)-Net over F₄ — Digital

Digital (28, 51, 68)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(51−23, 51, 883)-Net in Base 4 — Upper bound on s

There is no (28, 51, 884)-net in base 4, because

1 times m-reduction [i] would yield (28, 50, 884)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 272286 335498 940866 476526 339550 > 4⁵⁰ [i]