MinT - Best Known (56, 56+47, s)-Nets in Base 4

Best Known (56, 56+47, s)-Nets in Base 4

(56, 56+47, 90)-Net over F₄ — Constructive and digital

Digital (56, 103, 90)-net over F₄, using

1 times m-reduction [i] based on digital (56, 104, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 52, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(56, 56+47, 110)-Net over F₄ — Digital

Digital (56, 103, 110)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+47, 1451)-Net in Base 4 — Upper bound on s

There is no (56, 103, 1452)-net in base 4, because

1 times m-reduction [i] would yield (56, 102, 1452)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 25 912258 435119 807552 907472 916312 133133 457529 248703 497300 981988 > 4¹⁰² [i]