MinT - Best Known (48, 48+37, s)-Nets in Base 4

Best Known (48, 48+37, s)-Nets in Base 4

(48, 48+37, 98)-Net over F₄ — Constructive and digital

Digital (48, 85, 98)-net over F₄, using

1 times m-reduction [i] based on digital (48, 86, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 43, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(48, 48+37, 110)-Net over F₄ — Digital

Digital (48, 85, 110)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(48, 48+37, 1609)-Net in Base 4 — Upper bound on s

There is no (48, 85, 1610)-net in base 4, because

1 times m-reduction [i] would yield (48, 84, 1610)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 375 453564 473859 112423 788568 383639 118361 260228 508368 > 4⁸⁴ [i]