MinT - Best Known (7, 7+59, s)-Nets in Base 9

Best Known (7, 7+59, s)-Nets in Base 9

(7, 7+59, 36)-Net over F₉ — Constructive and digital

Digital (7, 66, 36)-net over F₉, using

net from sequence [i] based on digital (7, 35)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
  - a function field by SÃ©mirat [i]

(7, 7+59, 40)-Net over F₉ — Digital

Digital (7, 66, 40)-net over F₉, using

net from sequence [i] based on digital (7, 39)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 40, using
  - a curve from the manYPoints database [i]

(7, 7+59, 74)-Net in Base 9 — Upper bound on s

There is no (7, 66, 75)-net in base 9, because

1 times m-reduction [i] would yield (7, 65, 75)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9⁶⁵, 75, S₉, 58), but
  - the linear programming bound shows that MÂ â‰¥ 9194 385609 187547 917382 908043 398611 078466 117225 351467 455611 567465 680939 / 76 340336 > 9⁶⁵ [i]