MinT - Best Known (64−53, 64, s)-Nets in Base 9

Best Known (64−53, 64, s)-Nets in Base 9

(64−53, 64, 40)-Net over F₉ — Constructive and digital

Digital (11, 64, 40)-net over F₉, using

t-expansion [i] based on digital (8, 64, 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]

(64−53, 64, 55)-Net over F₉ — Digital

Digital (11, 64, 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]

(64−53, 64, 229)-Net in Base 9 — Upper bound on s

There is no (11, 64, 230)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶⁴, 230, S₉, 53), but
- the linear programming bound shows that MÂ â‰¥ 81 593973 187344 150965 516401 188161 740602 309710 783498 710941 952660 468707 525292 449932 947166 245122 025443 806271 783669 893299 459630 884995 126126 250000 / 6 838007 316757 736845 031405 465677 458994 568805 931785 321004 933751 549745 630354 787063 > 9⁶⁴ [i]