MinT - Best Known (59, 59+69, s)-Nets in Base 8

Best Known (59, 59+69, s)-Nets in Base 8

(59, 59+69, 113)-Net over F₈ — Constructive and digital

Digital (59, 128, 113)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (11, 45, 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, 83, 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]

(59, 59+69, 158)-Net over F₈ — Digital

Digital (59, 128, 158)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+69, 4546)-Net in Base 8 — Upper bound on s

There is no (59, 128, 4547)-net in base 8, because

1 times m-reduction [i] would yield (59, 127, 4547)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 953495 231997 864346 915577 989583 093891 443563 129864 888281 186008 909252 389617 352957 973766 945386 761173 916112 110467 696570 > 8¹²⁷ [i]