MinT - Best Known (8, 8+45, s)-Nets in Base 9

Best Known (8, 8+45, s)-Nets in Base 9

(8, 8+45, 40)-Net over F₉ — Constructive and digital

Digital (8, 53, 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]

(8, 8+45, 42)-Net over F₉ — Digital

Digital (8, 53, 42)-net over F₉, using

net from sequence [i] based on digital (8, 41)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 42, using
  - a curve from the manYPoints database [i]

(8, 8+45, 166)-Net in Base 9 — Upper bound on s

There is no (8, 53, 167)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁵³, 167, S₉, 45), but
- the linear programming bound shows that MÂ â‰¥ 1288 057564 800404 545817 478702 590070 254623 206398 067106 607992 756533 753857 272182 232454 692195 496510 109375 / 3 172135 471353 632797 174748 490493 094089 164917 704711 > 9⁵³ [i]