MinT - Best Known (63−51, 63, s)-Nets in Base 9

Best Known (63−51, 63, s)-Nets in Base 9

(63−51, 63, 40)-Net over F₉ — Constructive and digital

Digital (12, 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]

(63−51, 63, 56)-Net over F₉ — Digital

Digital (12, 63, 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]

(63−51, 63, 263)-Net in Base 9 — Upper bound on s

There is no (12, 63, 264)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶³, 264, S₉, 51), but
- the linear programming bound shows that MÂ â‰¥ 1 012511 546205 214638 076775 162565 093022 297702 109628 548386 524745 707083 520942 493011 143025 863773 121193 851874 326151 285819 584992 106620 159331 250000 / 712092 469099 247225 310609 006526 476416 497988 245654 113579 596337 815361 187230 775847 > 9⁶³ [i]