MinT - Best Known (149−55, 149, s)-Nets in Base 8

Best Known (149−55, 149, s)-Nets in Base 8

(149−55, 149, 354)-Net over F₈ — Constructive and digital

Digital (94, 149, 354)-net over F₈, using

t-expansion [i] based on digital (93, 149, 354)-net over F₈, using
- 23 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, 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]

(149−55, 149, 514)-Net in Base 8 — Constructive

(94, 149, 514)-net in base 8, using

1 times m-reduction [i] based on (94, 150, 514)-net in base 8, using
- trace code for nets [i] based on (19, 75, 257)-net in base 64, using
  - 1 times m-reduction [i] based on (19, 76, 257)-net in base 64, using
    - base change [i] based on digital (0, 57, 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]

(149−55, 149, 949)-Net over F₈ — Digital

Digital (94, 149, 949)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−55, 149, 139164)-Net in Base 8 — Upper bound on s

There is no (94, 149, 139165)-net in base 8, because

1 times m-reduction [i] would yield (94, 148, 139165)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 435485 011399 462815 751576 080574 024230 065878 170104 679103 338082 234211 209344 327868 223629 328236 012732 531457 899911 450782 930077 930087 934420 > 8¹⁴⁸ [i]