MinT - Best Known (51−22, 51, s)-Nets in Base 4

Best Known (51−22, 51, s)-Nets in Base 4

(51−22, 51, 76)-Net over F₄ — Constructive and digital

Digital (29, 51, 76)-net over F₄, using

1 times m-reduction [i] based on digital (29, 52, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 26, 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]

(51−22, 51, 78)-Net over F₄ — Digital

Digital (29, 51, 78)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(51−22, 51, 1003)-Net in Base 4 — Upper bound on s

There is no (29, 51, 1004)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5 095339 579573 162767 005969 734123 > 4⁵¹ [i]