MinT - Best Known (140−76, 140, s)-Nets in Base 8

Best Known (140−76, 140, s)-Nets in Base 8

(140−76, 140, 113)-Net over F₈ — Constructive and digital

Digital (64, 140, 113)-net over F₈, using

2 times m-reduction [i] based on digital (64, 142, 113)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 50, 48)-net over F₈, using
    - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, 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]

(140−76, 140, 165)-Net over F₈ — Digital

Digital (64, 140, 165)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−76, 140, 4535)-Net in Base 8 — Upper bound on s

There is no (64, 140, 4536)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 725662 312856 492741 895143 768553 519400 239242 764271 630703 974057 339917 820044 595548 862090 408331 594223 982552 955964 253343 603658 900865 > 8¹⁴⁰ [i]