MinT - Best Known (133−63, 133, s)-Nets in Base 4

Best Known (133−63, 133, s)-Nets in Base 4

(133−63, 133, 76)-Net over F₄ — Constructive and digital

Digital (70, 133, 76)-net over F₄, using

1 times m-reduction [i] based on digital (70, 134, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 67, 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]

(133−63, 133, 120)-Net over F₄ — Digital

Digital (70, 133, 120)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−63, 133, 1490)-Net in Base 4 — Upper bound on s

There is no (70, 133, 1491)-net in base 4, because

1 times m-reduction [i] would yield (70, 132, 1491)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 30 125923 761791 261785 636943 604929 615718 691921 096951 333893 469800 993911 321407 992832 > 4¹³² [i]