MinT - Best Known (56, 56+23, s)-Nets in Base 4

Best Known (56, 56+23, s)-Nets in Base 4

(56, 56+23, 312)-Net over F₄ — Constructive and digital

Digital (56, 79, 312)-net over F₄, using

4¹ times duplication [i] based on digital (55, 78, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 26, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(56, 56+23, 449)-Net over F₄ — Digital

Digital (56, 79, 449)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+23, 30403)-Net in Base 4 — Upper bound on s

There is no (56, 79, 30404)-net in base 4, because

1 times m-reduction [i] would yield (56, 78, 30404)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 91364 493997 614574 900355 962564 691759 291024 430328 > 4⁷⁸ [i]