MinT - Best Known (93−43, 93, s)-Nets in Base 4

Best Known (93−43, 93, s)-Nets in Base 4

(93−43, 93, 76)-Net over F₄ — Constructive and digital

Digital (50, 93, 76)-net over F₄, using

1 times m-reduction [i] based on digital (50, 94, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 47, 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]

(93−43, 93, 97)-Net over F₄ — Digital

Digital (50, 93, 97)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−43, 93, 1239)-Net in Base 4 — Upper bound on s

There is no (50, 93, 1240)-net in base 4, because

1 times m-reduction [i] would yield (50, 92, 1240)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 24 923160 865868 156838 744745 002597 568043 943739 140109 542751 > 4⁹² [i]