MinT - Best Known (136−76, 136, s)-Nets in Base 8

Best Known (136−76, 136, s)-Nets in Base 8

(136−76, 136, 100)-Net over F₈ — Constructive and digital

Digital (60, 136, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 46, 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 (14, 90, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]

(136−76, 136, 144)-Net over F₈ — Digital

Digital (60, 136, 144)-net over F₈, using

t-expansion [i] based on digital (45, 136, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(136−76, 136, 150)-Net in Base 8

(60, 136, 150)-net in base 8, using

base change [i] based on digital (26, 102, 150)-net over F₁₆, using
- net from sequence [i] based on digital (26, 149)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 26 and N(F) ≥ 150, using
    - a curve from the manYPoints database [i]

(136−76, 136, 3638)-Net in Base 8 — Upper bound on s

There is no (60, 136, 3639)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 661 411285 357974 444951 516957 892717 156446 834313 878245 005336 098768 240722 824588 604038 138208 179921 552898 839956 724939 964504 255515 > 8¹³⁶ [i]