MinT - Best Known (82−72, 82, s)-Nets in Base 9

Best Known (82−72, 82, s)-Nets in Base 9

(82−72, 82, 40)-Net over F₉ — Constructive and digital

Digital (10, 82, 40)-net over F₉, using

t-expansion [i] based on digital (8, 82, 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]

(82−72, 82, 54)-Net over F₉ — Digital

Digital (10, 82, 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]

(82−72, 82, 109)-Net in Base 9 — Upper bound on s

There is no (10, 82, 110)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁸², 110, S₉, 72), but
- the linear programming bound shows that MÂ â‰¥ 4927 033665 938247 365292 864466 687051 436651 637290 004635 265056 775049 647490 448563 447073 343189 087089 525706 413115 / 2611 112236 928540 623231 465967 > 9⁸² [i]