MinT - Best Known (90, 90+62, s)-Nets in Base 8

Best Known (90, 90+62, s)-Nets in Base 8

(90, 90+62, 354)-Net over F₈ — Constructive and digital

Digital (90, 152, 354)-net over F₈, using

14 times m-reduction [i] based on digital (90, 166, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 83, 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]

(90, 90+62, 384)-Net in Base 8 — Constructive

(90, 152, 384)-net in base 8, using

trace code for nets [i] based on (14, 76, 192)-net in base 64, using
- 1 times m-reduction [i] based on (14, 77, 192)-net in base 64, using
  - base change [i] based on digital (3, 66, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(90, 90+62, 590)-Net over F₈ — Digital

Digital (90, 152, 590)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+62, 47512)-Net in Base 8 — Upper bound on s

There is no (90, 152, 47513)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186083 091483 882555 763879 003545 591672 417315 726941 450235 581449 703895 224419 427974 575112 613531 794847 336022 116771 921697 626075 626816 925933 169792 > 8¹⁵² [i]