MinT - Best Known (116−90, 116, s)-Nets in Base 8

Best Known (116−90, 116, s)-Nets in Base 8

(116−90, 116, 65)-Net over F₈ — Constructive and digital

Digital (26, 116, 65)-net over F₈, using

t-expansion [i] based on digital (14, 116, 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]

(116−90, 116, 86)-Net over F₈ — Digital

Digital (26, 116, 86)-net over F₈, using

t-expansion [i] based on digital (25, 116, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(116−90, 116, 507)-Net in Base 8 — Upper bound on s

There is no (26, 116, 508)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 579 789444 998676 411566 445209 412795 494817 940125 546988 647483 987144 439248 738524 609573 124937 297594 736965 079396 > 8¹¹⁶ [i]