MinT - Best Known (35−31, 35, s)-Nets in Base 9

Best Known (35−31, 35, s)-Nets in Base 9

(35−31, 35, 30)-Net over F₉ — Constructive and digital

Digital (4, 35, 30)-net over F₉, using

net from sequence [i] based on digital (4, 29)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
  - a function field by SÃ©mirat [i]

(35−31, 35, 84)-Net in Base 9 — Upper bound on s

There is no (4, 35, 85)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9³⁵, 85, S₉, 31), but
- the linear programming bound shows that MÂ â‰¥ 112620 123087 737061 231244 499443 215625 747636 066957 184847 246285 / 44 721454 781644 057928 595589 > 9³⁵ [i]