MinT - Best Known (63−52, 63, s)-Nets in Base 9

Best Known (63−52, 63, s)-Nets in Base 9

(63−52, 63, 40)-Net over F₉ — Constructive and digital

Digital (11, 63, 40)-net over F₉, using

t-expansion [i] based on digital (8, 63, 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]

(63−52, 63, 55)-Net over F₉ — Digital

Digital (11, 63, 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]

(63−52, 63, 232)-Net in Base 9 — Upper bound on s

There is no (11, 63, 233)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶³, 233, S₉, 52), but
- the linear programming bound shows that MÂ â‰¥ 603867 883130 706268 568168 104002 697686 603318 804513 783072 334610 686593 323969 449615 119237 466337 136159 511448 681581 513069 943167 205793 074072 611125 / 444446 085403 020587 018435 878807 753494 502087 375998 145327 465886 982120 425187 597973 > 9⁶³ [i]