MinT - Best Known (256−85, 256, s)-Nets in Base 4

Best Known (256−85, 256, s)-Nets in Base 4

(256−85, 256, 450)-Net over F₄ — Constructive and digital

Digital (171, 256, 450)-net over F₄, using

t-expansion [i] based on digital (170, 256, 450)-net over F₄, using
- 4 times m-reduction [i] based on digital (170, 260, 450)-net over F₄, using
  - trace code for nets [i] based on digital (40, 130, 225)-net over F₁₆, using
    - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
        a function field by GarcÃa and Quoos [i]

(256−85, 256, 694)-Net over F₄ — Digital

Digital (171, 256, 694)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−85, 256, 24856)-Net in Base 4 — Upper bound on s

There is no (171, 256, 24857)-net in base 4, because

1 times m-reduction [i] would yield (171, 255, 24857)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3353 867863 206722 304528 163581 926679 292759 122919 475263 451080 351682 733388 216074 481680 236356 381611 333927 073498 349068 610717 153321 932731 054218 339594 061562 146880 > 4²⁵⁵ [i]