MinT - Best Known (10, 80, s)-Nets in Base 9

Best Known (10, 80, s)-Nets in Base 9

(10, 80, 40)-Net over F₉ — Constructive and digital

Digital (10, 80, 40)-net over F₉, using

t-expansion [i] based on digital (8, 80, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(10, 80, 54)-Net over F₉ — Digital

Digital (10, 80, 54)-net over F₉, using

net from sequence [i] based on digital (10, 53)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
  - a curve from the manYPoints database [i]

(10, 80, 124)-Net in Base 9 — Upper bound on s

There is no (10, 80, 125)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁸⁰, 125, S₉, 70), but
- the linear programming bound shows that MÂ â‰¥ 18558 176820 065823 206140 092974 499733 392292 523040 911134 657074 958621 232760 859886 828641 654476 046552 900071 236906 882636 356298 744418 / 842349 023115 687520 400915 764890 590473 996502 968505 > 9⁸⁰ [i]