MinT - Best Known (96−49, 96, s)-Nets in Base 8

Best Known (96−49, 96, s)-Nets in Base 8

(96−49, 96, 110)-Net over F₈ — Constructive and digital

Digital (47, 96, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 33, 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, 63, 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]

(96−49, 96, 155)-Net over F₈ — Digital

Digital (47, 96, 155)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(96−49, 96, 5245)-Net in Base 8 — Upper bound on s

There is no (47, 96, 5246)-net in base 8, because

1 times m-reduction [i] would yield (47, 95, 5246)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 62 390584 811305 437855 630991 114897 905365 550080 292551 663951 447582 513927 181723 636174 956221 > 8⁹⁵ [i]