MinT - Best Known (101, 101+54, s)-Nets in Base 8

Best Known (101, 101+54, s)-Nets in Base 8

(101, 101+54, 382)-Net over F₈ — Constructive and digital

Digital (101, 155, 382)-net over F₈, using

1 times m-reduction [i] based on digital (101, 156, 382)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 32, 28)-net over F₈, using
    - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
        a function field by SÃ©mirat [i]
  2. digital (69, 124, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 62, 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]

(101, 101+54, 576)-Net in Base 8 — Constructive

(101, 155, 576)-net in base 8, using

5 times m-reduction [i] based on (101, 160, 576)-net in base 8, using
- trace code for nets [i] based on (21, 80, 288)-net in base 64, using
  - 4 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
    - base change [i] based on digital (9, 72, 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]

(101, 101+54, 1314)-Net over F₈ — Digital

Digital (101, 155, 1314)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+54, 238607)-Net in Base 8 — Upper bound on s

There is no (101, 155, 238608)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 276911 208204 574306 322637 935956 048306 583409 652704 349144 926166 678169 576797 949836 041930 553932 992182 489987 313266 436153 531179 084779 175566 652352 > 8¹⁵⁵ [i]