MinT - Best Known (44−35, 44, s)-Nets in Base 9

Best Known (44−35, 44, s)-Nets in Base 9

(44−35, 44, 40)-Net over F₉ — Constructive and digital

Digital (9, 44, 40)-net over F₉, using

t-expansion [i] based on digital (8, 44, 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]

(44−35, 44, 48)-Net over F₉ — Digital

Digital (9, 44, 48)-net over F₉, using

net from sequence [i] based on digital (9, 47)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 9 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(44−35, 44, 221)-Net in Base 9 — Upper bound on s

There is no (9, 44, 222)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁴⁴, 222, S₉, 35), but
- the linear programming bound shows that MÂ â‰¥ 257 571198 764138 869006 198844 023212 542986 962342 353608 393838 923774 516310 648720 747218 944000 / 261 166390 002457 653281 041534 208520 277848 647443 > 9⁴⁴ [i]