MinT - Best Known (91, 134, s)-Nets in Base 8

Best Known (91, 134, s)-Nets in Base 8

(91, 134, 402)-Net over F₈ — Constructive and digital

Digital (91, 134, 402)-net over F₈, using

1 times m-reduction [i] based on digital (91, 135, 402)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 33, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
        a function field by SÃ©mirat [i]
  2. digital (58, 102, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 51, 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]

(91, 134, 576)-Net in Base 8 — Constructive

(91, 134, 576)-net in base 8, using

t-expansion [i] based on (89, 134, 576)-net in base 8, using
- 6 times m-reduction [i] based on (89, 140, 576)-net in base 8, using
  - trace code for nets [i] based on (19, 70, 288)-net in base 64, using
    - base change [i] based on digital (9, 60, 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]

(91, 134, 1816)-Net over F₈ — Digital

Digital (91, 134, 1816)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 134, 650063)-Net in Base 8 — Upper bound on s

There is no (91, 134, 650064)-net in base 8, because

1 times m-reduction [i] would yield (91, 133, 650064)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 291147 159406 243722 029778 422961 071053 768857 517564 979471 266027 461303 934660 793076 476139 224724 894837 205304 466783 052040 480676 > 8¹³³ [i]