MinT - Best Known (257−74, 257, s)-Nets in Base 4

Best Known (257−74, 257, s)-Nets in Base 4

(257−74, 257, 531)-Net over F₄ — Constructive and digital

Digital (183, 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]

(257−74, 257, 1222)-Net over F₄ — Digital

Digital (183, 257, 1222)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(257−74, 257, 74214)-Net in Base 4 — Upper bound on s

There is no (183, 257, 74215)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53642 312850 054889 655145 798674 448154 811488 809829 194802 672156 709739 138642 935353 032402 089462 795872 708535 014448 495850 934080 605072 146429 714962 261116 099780 097274 > 4²⁵⁷ [i]