MinT - Best Known (58, 58+24, s)-Nets in Base 8

Best Known (58, 58+24, s)-Nets in Base 8

(58, 58+24, 389)-Net over F₈ — Constructive and digital

Digital (58, 82, 389)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 20, 35)-net over F₈, using
  - net from sequence [i] based on digital (8, 34)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 7, N(F)Â =Â 34, and 1 place with degree 2 [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 (38, 62, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 31, 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]

(58, 58+24, 576)-Net in Base 8 — Constructive

(58, 82, 576)-net in base 8, using

t-expansion [i] based on (57, 82, 576)-net in base 8, using
- 2 times m-reduction [i] based on (57, 84, 576)-net in base 8, using
  - trace code for nets [i] based on (15, 42, 288)-net in base 64, using
    - base change [i] based on digital (9, 36, 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]

(58, 58+24, 2245)-Net over F₈ — Digital

Digital (58, 82, 2245)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+24, 1120406)-Net in Base 8 — Upper bound on s

There is no (58, 82, 1120407)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 113 079228 055567 506719 805916 710979 125311 615789 640124 127097 187401 321173 875686 > 8⁸² [i]