MinT - Best Known (112−60, 112, s)-Nets in Base 8

Best Known (112−60, 112, s)-Nets in Base 8

(112−60, 112, 100)-Net over F₈ — Constructive and digital

Digital (52, 112, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 38, 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, 74, 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]

(112−60, 112, 145)-Net over F₈ — Digital

Digital (52, 112, 145)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−60, 112, 4029)-Net in Base 8 — Upper bound on s

There is no (52, 112, 4030)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 140909 031844 757550 880083 772783 290449 722546 510974 084973 424216 304735 388732 559516 466016 754987 091099 099520 > 8¹¹² [i]