MinT - Best Known (257−71, 257, s)-Nets in Base 4

Best Known (257−71, 257, s)-Nets in Base 4

(257−71, 257, 531)-Net over F₄ — Constructive and digital

Digital (186, 257, 531)-net over F₄, using

t-expansion [i] based on digital (179, 257, 531)-net over F₄, using
- 1 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]

(257−71, 257, 1464)-Net over F₄ — Digital

Digital (186, 257, 1464)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−71, 257, 117401)-Net in Base 4 — Upper bound on s

There is no (186, 257, 117402)-net in base 4, because

1 times m-reduction [i] would yield (186, 256, 117402)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13408 010582 807705 382755 637704 774353 086204 865399 018974 026475 170613 576088 627482 838170 279402 544857 830330 676345 318541 094725 551192 902643 168807 522813 263186 016592 > 4²⁵⁶ [i]