MinT - Best Known (104, 104+54, s)-Nets in Base 8

Best Known (104, 104+54, s)-Nets in Base 8

(104, 104+54, 399)-Net over F₈ — Constructive and digital

Digital (104, 158, 399)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 36, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]
2. digital (68, 122, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 61, 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]

(104, 104+54, 576)-Net in Base 8 — Constructive

(104, 158, 576)-net in base 8, using

8 times m-reduction [i] based on (104, 166, 576)-net in base 8, using
- trace code for nets [i] based on (21, 83, 288)-net in base 64, using
  - 1 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]

(104, 104+54, 1475)-Net over F₈ — Digital

Digital (104, 158, 1475)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+54, 300630)-Net in Base 8 — Upper bound on s

There is no (104, 158, 300631)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48779 048317 056986 563933 502093 385997 712884 889129 376018 444785 404137 529918 638283 262643 735851 602049 443818 370641 737980 701795 915767 744254 362552 328992 > 8¹⁵⁸ [i]