MinT - Best Known (43, 43+45, s)-Nets in Base 8

Best Known (43, 43+45, s)-Nets in Base 8

(43, 43+45, 99)-Net over F₈ — Constructive and digital

Digital (43, 88, 99)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (7, 29, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [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, 59, 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]

(43, 43+45, 144)-Net over F₈ — Digital

Digital (43, 88, 144)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+45, 4806)-Net in Base 8 — Upper bound on s

There is no (43, 88, 4807)-net in base 8, because

1 times m-reduction [i] would yield (43, 87, 4807)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 712578 105870 314107 462719 303493 506421 101634 273236 711582 670889 085060 341201 472292 > 8⁸⁷ [i]