MinT - Best Known (100−37, 100, s)-Nets in Base 8

Best Known (100−37, 100, s)-Nets in Base 8

(100−37, 100, 354)-Net over F₈ — Constructive and digital

Digital (63, 100, 354)-net over F₈, using

12 times m-reduction [i] based on digital (63, 112, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 56, 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]

(100−37, 100, 514)-Net in Base 8 — Constructive

(63, 100, 514)-net in base 8, using

base change [i] based on digital (38, 75, 514)-net over F₁₆, using
- 1 times m-reduction [i] based on digital (38, 76, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 38, 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]

(100−37, 100, 676)-Net over F₈ — Digital

Digital (63, 100, 676)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−37, 100, 99995)-Net in Base 8 — Upper bound on s

There is no (63, 100, 99996)-net in base 8, because

1 times m-reduction [i] would yield (63, 99, 99996)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 254669 212432 135231 436780 678431 226999 043225 419177 317178 437017 444098 671378 028627 548094 160737 > 8⁹⁹ [i]