MinT - Best Known (93−47, 93, s)-Nets in Base 8

Best Known (93−47, 93, s)-Nets in Base 8

(93−47, 93, 110)-Net over F₈ — Constructive and digital

Digital (46, 93, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 32, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]
2. digital (14, 61, 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]

(93−47, 93, 158)-Net over F₈ — Digital

Digital (46, 93, 158)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−47, 93, 5502)-Net in Base 8 — Upper bound on s

There is no (46, 93, 5503)-net in base 8, because

1 times m-reduction [i] would yield (46, 92, 5503)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 121457 868843 347235 620853 185978 531331 573469 621922 158373 230923 998670 244961 863188 470496 > 8⁹² [i]