MinT - Best Known (56, 56+45, s)-Nets in Base 4

Best Known (56, 56+45, s)-Nets in Base 4

(56, 56+45, 98)-Net over F₄ — Constructive and digital

Digital (56, 101, 98)-net over F₄, using

1 times m-reduction [i] based on digital (56, 102, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 51, 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]

(56, 56+45, 116)-Net over F₄ — Digital

Digital (56, 101, 116)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+45, 1628)-Net in Base 4 — Upper bound on s

There is no (56, 101, 1629)-net in base 4, because

1 times m-reduction [i] would yield (56, 100, 1629)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 628407 465345 097290 638669 917105 233305 143307 159743 426298 687940 > 4¹⁰⁰ [i]