MinT - Best Known (106−56, 106, s)-Nets in Base 8

Best Known (106−56, 106, s)-Nets in Base 8

(106−56, 106, 100)-Net over F₈ — Constructive and digital

Digital (50, 106, 100)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (8, 36, 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, 70, 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]

(106−56, 106, 146)-Net over F₈ — Digital

Digital (50, 106, 146)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−56, 106, 4216)-Net in Base 8 — Upper bound on s

There is no (50, 106, 4217)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 535796 991849 320258 819109 736653 436311 654841 574854 478978 619302 759592 536091 070830 409370 445219 418824 > 8¹⁰⁶ [i]