MinT - Best Known (67, 67+88, s)-Nets in Base 8

Best Known (67, 67+88, s)-Nets in Base 8

(67, 67+88, 110)-Net over F₈ — Constructive and digital

Digital (67, 155, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 53, 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, 102, 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]

(67, 67+88, 151)-Net over F₈ — Digital

Digital (67, 155, 151)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+88, 156)-Net in Base 8

(67, 155, 156)-net in base 8, using

5 times m-reduction [i] based on (67, 160, 156)-net in base 8, using
- base change [i] based on digital (27, 120, 156)-net over F₁₆, using
  - net from sequence [i] based on digital (27, 155)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 27 and N(F) ≥ 156, using
      - a curve from the manYPoints database [i]

(67, 67+88, 3714)-Net in Base 8 — Upper bound on s

There is no (67, 155, 3715)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 493349 322594 855407 220304 594877 185725 248174 925560 792780 908263 554444 120622 756925 131340 459960 457658 724794 344868 968983 623063 188332 686564 552544 > 8¹⁵⁵ [i]