MinT - Best Known (65−53, 65, s)-Nets in Base 9

Best Known (65−53, 65, s)-Nets in Base 9

(65−53, 65, 40)-Net over F₉ — Constructive and digital

Digital (12, 65, 40)-net over F₉, using

t-expansion [i] based on digital (8, 65, 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]

(65−53, 65, 56)-Net over F₉ — Digital

Digital (12, 65, 56)-net over F₉, using

net from sequence [i] based on digital (12, 55)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 12 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(65−53, 65, 257)-Net in Base 9 — Upper bound on s

There is no (12, 65, 258)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶⁵, 258, S₉, 53), but
- the linear programming bound shows that MÂ â‰¥ 3115 168854 220783 215219 768780 159936 720843 927087 163333 700130 000830 275274 104131 449440 559940 656772 807198 649003 636302 225680 570591 397494 949207 472122 873600 / 27 533585 604222 238879 620126 549314 600127 207589 391129 267721 230267 333962 835368 350738 616937 > 9⁶⁵ [i]