MinT - Best Known (63, 63+82, s)-Nets in Base 8

Best Known (63, 63+82, s)-Nets in Base 8

(63, 63+82, 100)-Net over F₈ — Constructive and digital

Digital (63, 145, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 49, 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, 96, 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]

(63, 63+82, 145)-Net over F₈ — Digital

Digital (63, 145, 145)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+82, 150)-Net in Base 8

(63, 145, 150)-net in base 8, using

3 times m-reduction [i] based on (63, 148, 150)-net in base 8, using
- base change [i] based on digital (26, 111, 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]

(63, 63+82, 3577)-Net in Base 8 — Upper bound on s

There is no (63, 145, 3578)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 89491 604852 114555 067151 266295 696452 123038 704422 549642 540221 820958 270648 568984 673709 623855 985702 910589 482030 787082 954267 199781 272901 > 8¹⁴⁵ [i]