MinT - Best Known (49, 49+54, s)-Nets in Base 8

Best Known (49, 49+54, s)-Nets in Base 8

(49, 49+54, 100)-Net over F₈ — Constructive and digital

Digital (49, 103, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 35, 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, 68, 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]

(49, 49+54, 147)-Net over F₈ — Digital

Digital (49, 103, 147)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+54, 4332)-Net in Base 8 — Upper bound on s

There is no (49, 103, 4333)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1045 766936 240015 446810 246077 055402 672840 245246 216353 146814 575425 184588 945094 938146 648821 616888 > 8¹⁰³ [i]