MinT - Best Known (256−73, 256, s)-Nets in Base 4

Best Known (256−73, 256, s)-Nets in Base 4

(256−73, 256, 531)-Net over F₄ — Constructive and digital

Digital (183, 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]

(256−73, 256, 1269)-Net over F₄ — Digital

Digital (183, 256, 1269)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−73, 256, 87510)-Net in Base 4 — Upper bound on s

There is no (183, 256, 87511)-net in base 4, because

1 times m-reduction [i] would yield (183, 255, 87511)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3352 387101 814125 738257 353758 470591 763298 833527 908310 046832 427237 356345 267697 890695 205690 625293 561722 514611 374252 770584 376178 023914 761743 059071 461943 043418 > 4²⁵⁵ [i]