MinT - Best Known (63, 63+30, s)-Nets in Base 8

Best Known (63, 63+30, s)-Nets in Base 8

(63, 63+30, 379)-Net over F₈ — Constructive and digital

Digital (63, 93, 379)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 19, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]
2. digital (44, 74, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 37, 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]

(63, 63+30, 576)-Net in Base 8 — Constructive

(63, 93, 576)-net in base 8, using

1 times m-reduction [i] based on (63, 94, 576)-net in base 8, using
- trace code for nets [i] based on (16, 47, 288)-net in base 64, using
  - 2 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
    - base change [i] based on digital (9, 42, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(63, 63+30, 1327)-Net over F₈ — Digital

Digital (63, 93, 1327)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+30, 364599)-Net in Base 8 — Upper bound on s

There is no (63, 93, 364600)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 971369 154971 325865 172557 644412 387887 301027 107061 953239 510310 691102 610598 450002 151586 > 8⁹³ [i]