MinT - Best Known (139−78, 139, s)-Nets in Base 8

Best Known (139−78, 139, s)-Nets in Base 8

(139−78, 139, 100)-Net over F₈ — Constructive and digital

Digital (61, 139, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 47, 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, 92, 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]

(139−78, 139, 144)-Net over F₈ — Digital

Digital (61, 139, 144)-net over F₈, using

t-expansion [i] based on digital (45, 139, 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]

(139−78, 139, 150)-Net in Base 8

(61, 139, 150)-net in base 8, using

1 times m-reduction [i] based on (61, 140, 150)-net in base 8, using
- base change [i] based on digital (26, 105, 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]

(139−78, 139, 3614)-Net in Base 8 — Upper bound on s

There is no (61, 139, 3615)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 338815 378554 698022 194202 596839 110747 774382 410213 510728 124590 220694 420997 567242 345500 022317 315149 684787 552653 050932 819402 461952 > 8¹³⁹ [i]