MinT - Best Known (94, 94+49, s)-Nets in Base 8

Best Known (94, 94+49, s)-Nets in Base 8

(94, 94+49, 388)-Net over F₈ — Constructive and digital

Digital (94, 143, 388)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (7, 31, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]
2. digital (63, 112, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 56, 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]

(94, 94+49, 576)-Net in Base 8 — Constructive

(94, 143, 576)-net in base 8, using

5 times m-reduction [i] based on (94, 148, 576)-net in base 8, using
- trace code for nets [i] based on (20, 74, 288)-net in base 64, using
  - 3 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
    - base change [i] based on digital (9, 66, 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]

(94, 94+49, 1337)-Net over F₈ — Digital

Digital (94, 143, 1337)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+49, 308692)-Net in Base 8 — Upper bound on s

There is no (94, 143, 308693)-net in base 8, because

1 times m-reduction [i] would yield (94, 142, 308693)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 298215 286460 085619 497577 066709 374755 573245 961397 599261 970867 803158 611250 884933 037687 267505 402984 540785 475763 705472 938134 874472 > 8¹⁴² [i]