MinT - Best Known (247−66, 247, s)-Nets in Base 4

Best Known (247−66, 247, s)-Nets in Base 4

(247−66, 247, 531)-Net over F₄ — Constructive and digital

Digital (181, 247, 531)-net over F₄, using

t-expansion [i] based on digital (179, 247, 531)-net over F₄, using
- 11 times m-reduction [i] based on digital (179, 258, 531)-net over F₄, using
  - trace code for nets [i] based on digital (7, 86, 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]

(247−66, 247, 576)-Net in Base 4 — Constructive

(181, 247, 576)-net in base 4, using

2 times m-reduction [i] based on (181, 249, 576)-net in base 4, using
- trace code for nets [i] based on (15, 83, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
    - base change [i] based on digital (3, 72, 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]

(247−66, 247, 1647)-Net over F₄ — Digital

Digital (181, 247, 1647)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−66, 247, 140759)-Net in Base 4 — Upper bound on s

There is no (181, 247, 140760)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51154 026351 555187 071130 911423 665448 423734 910358 333445 815640 198788 895132 699007 729663 417563 668970 304012 544318 199232 052789 656060 649484 228047 387311 377998 > 4²⁴⁷ [i]