MinT - Best Known (95−34, 95, s)-Nets in Base 8

Best Known (95−34, 95, s)-Nets in Base 8

(95−34, 95, 354)-Net over F₈ — Constructive and digital

Digital (61, 95, 354)-net over F₈, using

13 times m-reduction [i] based on digital (61, 108, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 54, 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]

(95−34, 95, 516)-Net in Base 8 — Constructive

(61, 95, 516)-net in base 8, using

1 times m-reduction [i] based on (61, 96, 516)-net in base 8, using
- base change [i] based on digital (37, 72, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 36, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(95−34, 95, 765)-Net over F₈ — Digital

Digital (61, 95, 765)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−34, 95, 114152)-Net in Base 8 — Upper bound on s

There is no (61, 95, 114153)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 62 166611 822547 479557 739303 834022 855047 481682 628381 264595 513814 134937 145753 268091 994144 > 8⁹⁵ [i]