MinT - Best Known (58, 58+63, s)-Nets in Base 8

Best Known (58, 58+63, s)-Nets in Base 8

(58, 58+63, 113)-Net over F₈ — Constructive and digital

Digital (58, 121, 113)-net over F₈, using

3 times m-reduction [i] based on digital (58, 124, 113)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 44, 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, 80, 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]

(58, 58+63, 173)-Net over F₈ — Digital

Digital (58, 121, 173)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+63, 5536)-Net in Base 8 — Upper bound on s

There is no (58, 121, 5537)-net in base 8, because

1 times m-reduction [i] would yield (58, 120, 5537)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 353069 783849 221731 636955 310863 172459 473130 996306 087948 327447 740174 887719 068118 652129 642262 315223 967506 917600 > 8¹²⁰ [i]