MinT - Best Known (46, 85, s)-Nets in Base 4

Best Known (46, 85, s)-Nets in Base 4

(46, 85, 76)-Net over F₄ — Constructive and digital

Digital (46, 85, 76)-net over F₄, using

1 times m-reduction [i] based on digital (46, 86, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 43, 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]

(46, 85, 93)-Net over F₄ — Digital

Digital (46, 85, 93)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 85, 1197)-Net in Base 4 — Upper bound on s

There is no (46, 85, 1198)-net in base 4, because

1 times m-reduction [i] would yield (46, 84, 1198)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 376 118627 456732 381576 402545 568678 655841 402285 361236 > 4⁸⁴ [i]