MinT - Best Known (59−48, 59, s)-Nets in Base 9

Best Known (59−48, 59, s)-Nets in Base 9

(59−48, 59, 40)-Net over F₉ — Constructive and digital

Digital (11, 59, 40)-net over F₉, using

t-expansion [i] based on digital (8, 59, 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]

(59−48, 59, 55)-Net over F₉ — Digital

Digital (11, 59, 55)-net over F₉, using

net from sequence [i] based on digital (11, 54)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 11 and N(F) ≥ 55, using
  - a curve from the manYPoints database [i]

(59−48, 59, 241)-Net in Base 9 — Upper bound on s

There is no (11, 59, 242)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵⁹, 242, S₉, 48), but
- the linear programming bound shows that MÂ â‰¥ 843 039193 817398 359492 871522 560319 359046 172711 607118 999413 350912 169625 111775 135021 315003 897038 203069 558294 012233 163528 810284 640000 / 4 143287 847468 423402 964548 230537 815075 008586 023736 774827 467273 253690 036709 > 9⁵⁹ [i]