MinT - Best Known (85−30, 85, s)-Nets in Base 8

Best Known (85−30, 85, s)-Nets in Base 8

(85−30, 85, 354)-Net over F₈ — Constructive and digital

Digital (55, 85, 354)-net over F₈, using

11 times m-reduction [i] based on digital (55, 96, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 48, 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]

(85−30, 85, 516)-Net in Base 8 — Constructive

(55, 85, 516)-net in base 8, using

1 times m-reduction [i] based on (55, 86, 516)-net in base 8, using
- trace code for nets [i] based on (12, 43, 258)-net in base 64, using
  - 1 times m-reduction [i] based on (12, 44, 258)-net in base 64, using
    - base change [i] based on digital (1, 33, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(85−30, 85, 754)-Net over F₈ — Digital

Digital (55, 85, 754)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−30, 85, 120266)-Net in Base 8 — Upper bound on s

There is no (55, 85, 120267)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 57897 973173 744467 358319 289727 068911 536204 691840 250626 496431 058094 647265 369920 > 8⁸⁵ [i]