MinT - Best Known (73, 111, s)-Nets in Base 8

Best Known (73, 111, s)-Nets in Base 8

(73, 111, 371)-Net over F₈ — Constructive and digital

Digital (73, 111, 371)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (2, 21, 17)-net over F₈, using
  - net from sequence [i] based on digital (2, 16)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 2 and N(F) ≥ 17, using
      - a function field by SÃ©mirat [i]
2. digital (52, 90, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 45, 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]

(73, 111, 576)-Net in Base 8 — Constructive

(73, 111, 576)-net in base 8, using

1 times m-reduction [i] based on (73, 112, 576)-net in base 8, using
- trace code for nets [i] based on (17, 56, 288)-net in base 64, using
  - base change [i] based on digital (9, 48, 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]

(73, 111, 1090)-Net over F₈ — Digital

Digital (73, 111, 1090)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 111, 213816)-Net in Base 8 — Upper bound on s

There is no (73, 111, 213817)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 17499 377470 745312 306991 213053 571921 956949 858520 648406 620090 432822 639817 727484 385730 417821 696779 597640 > 8¹¹¹ [i]