MinT - Best Known (231−57, 231, s)-Nets in Base 4

Best Known (231−57, 231, s)-Nets in Base 4

(231−57, 231, 1028)-Net over F₄ — Constructive and digital

Digital (174, 231, 1028)-net over F₄, using

1 times m-reduction [i] based on digital (174, 232, 1028)-net over F₄, using
- trace code for nets [i] based on digital (0, 58, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(231−57, 231, 2231)-Net over F₄ — Digital

Digital (174, 231, 2231)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−57, 231, 332159)-Net in Base 4 — Upper bound on s

There is no (174, 231, 332160)-net in base 4, because

1 times m-reduction [i] would yield (174, 230, 332160)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 977251 135461 206166 644481 941052 925131 879330 289652 988330 391270 718939 437507 120116 305966 480478 771106 329531 568266 023131 702402 480639 392118 516457 > 4²³⁰ [i]