MinT - Best Known (92−80, 92, s)-Nets in Base 9

Best Known (92−80, 92, s)-Nets in Base 9

(92−80, 92, 40)-Net over F₉ — Constructive and digital

Digital (12, 92, 40)-net over F₉, using

t-expansion [i] based on digital (8, 92, 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]

(92−80, 92, 56)-Net over F₉ — Digital

Digital (12, 92, 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]

(92−80, 92, 144)-Net in Base 9 — Upper bound on s

There is no (12, 92, 145)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁹², 145, S₉, 80), but
- the linear programming bound shows that MÂ â‰¥ 1203 010884 112197 826174 713543 310030 026622 207125 012833 902424 619916 624931 373666 405183 335292 714127 591278 989842 948488 005697 968055 188690 527163 200105 186702 220616 668835 / 181966 553195 262368 567124 974245 924564 519444 129366 877829 186007 668750 376643 > 9⁹² [i]