MinT - Best Known (183−49, 183, s)-Nets in Base 4

Best Known (183−49, 183, s)-Nets in Base 4

(183−49, 183, 531)-Net over F₄ — Constructive and digital

Digital (134, 183, 531)-net over F₄, using

t-expansion [i] based on digital (133, 183, 531)-net over F₄, using
- 6 times m-reduction [i] based on digital (133, 189, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 63, 177)-net over F₆₄, using
    - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
        a function field by GarcÃa and Quoos [i]

(183−49, 183, 576)-Net in Base 4 — Constructive

(134, 183, 576)-net in base 4, using

trace code for nets [i] based on (12, 61, 192)-net in base 64, using
- 2 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
  - base change [i] based on digital (3, 54, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(183−49, 183, 1257)-Net over F₄ — Digital

Digital (134, 183, 1257)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(183−49, 183, 120169)-Net in Base 4 — Upper bound on s

There is no (134, 183, 120170)-net in base 4, because

1 times m-reduction [i] would yield (134, 182, 120170)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 583828 755054 957379 613285 279473 577316 892011 524350 194059 062200 271804 737732 976759 773834 193656 525133 511437 336374 > 4¹⁸² [i]