MinT - Best Known (98−76, 98, s)-Nets in Base 8

Best Known (98−76, 98, s)-Nets in Base 8

(98−76, 98, 65)-Net over F₈ — Constructive and digital

Digital (22, 98, 65)-net over F₈, using

t-expansion [i] based on digital (14, 98, 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]

(98−76, 98, 76)-Net over F₈ — Digital

Digital (22, 98, 76)-net over F₈, using

t-expansion [i] based on digital (20, 98, 76)-net over F₈, using
- net from sequence [i] based on digital (20, 75)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
    - a curve from the manYPoints database [i]

(98−76, 98, 434)-Net in Base 8 — Upper bound on s

There is no (22, 98, 435)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 33735 478165 287868 852589 901423 443202 381201 531629 706343 188159 521338 811592 892570 767633 933612 > 8⁹⁸ [i]