MinT - Best Known (90, 90+81, s)-Nets in Base 8

Best Known (90, 90+81, s)-Nets in Base 8

(90, 90+81, 208)-Net over F₈ — Constructive and digital

Digital (90, 171, 208)-net over F₈, using

t-expansion [i] based on digital (89, 171, 208)-net over F₈, using
- 1 times m-reduction [i] based on digital (89, 172, 208)-net over F₈, using
  - trace code for nets [i] based on digital (3, 86, 104)-net over F₆₄, using
    - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(90, 90+81, 225)-Net in Base 8 — Constructive

(90, 171, 225)-net in base 8, using

t-expansion [i] based on (83, 171, 225)-net in base 8, using
- 1 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
  - base change [i] based on digital (40, 129, 225)-net over F₁₆, using
    - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
        a function field by GarcÃa and Quoos [i]

(90, 90+81, 341)-Net over F₈ — Digital

Digital (90, 171, 341)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+81, 15492)-Net in Base 8 — Upper bound on s

There is no (90, 171, 15493)-net in base 8, because

1 times m-reduction [i] would yield (90, 170, 15493)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3356 853075 845333 282302 992997 257520 108242 509676 519470 547180 573723 047635 450198 918018 741390 782440 052550 188498 235406 418129 534462 322367 117403 272934 368821 027920 > 8¹⁷⁰ [i]