MinT - Best Known (256−71, 256, s)-Nets in Base 4

Best Known (256−71, 256, s)-Nets in Base 4

(256−71, 256, 531)-Net over F₄ — Constructive and digital

Digital (185, 256, 531)-net over F₄, using

t-expansion [i] based on digital (179, 256, 531)-net over F₄, using
- 2 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]

(256−71, 256, 1434)-Net over F₄ — Digital

Digital (185, 256, 1434)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−71, 256, 112841)-Net in Base 4 — Upper bound on s

There is no (185, 256, 112842)-net in base 4, because

1 times m-reduction [i] would yield (185, 255, 112842)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3352 347629 198269 723088 751284 125063 117996 333649 679474 400460 387598 309547 888951 457919 659835 675459 771557 298155 873534 992953 155797 965370 901336 035312 301398 001080 > 4²⁵⁵ [i]