MinT - Best Known (65−54, 65, s)-Nets in Base 9

Best Known (65−54, 65, s)-Nets in Base 9

(65−54, 65, 40)-Net over F₉ — Constructive and digital

Digital (11, 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]

(65−54, 65, 55)-Net over F₉ — Digital

Digital (11, 65, 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]

(65−54, 65, 224)-Net in Base 9 — Upper bound on s

There is no (11, 65, 225)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶⁵, 225, S₉, 54), but
- the linear programming bound shows that MÂ â‰¥ 1 407158 071957 405502 080634 170649 666681 351029 811313 477564 249946 509212 567552 061950 290997 535422 640957 000607 894786 170825 293062 081202 608589 929200 / 12919 598267 682231 631223 118900 223172 391171 482474 551992 207926 453044 062169 872017 > 9⁶⁵ [i]