MinT - Best Known (256−77, 256, s)-Nets in Base 4

Best Known (256−77, 256, s)-Nets in Base 4

(256−77, 256, 531)-Net over F₄ — Constructive and digital

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]

(256−77, 256, 1015)-Net over F₄ — Digital

Digital (179, 256, 1015)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(256−77, 256, 54900)-Net in Base 4 — Upper bound on s

There is no (179, 256, 54901)-net in base 4, because

1 times m-reduction [i] would yield (179, 255, 54901)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3353 519814 125016 185195 682507 235794 275214 692922 945907 543820 721944 199272 407919 907875 232319 691847 443902 841946 401943 630649 526328 085102 202690 997368 750523 001528 > 4²⁵⁵ [i]