MinT - Best Known (62−52, 62, s)-Nets in Base 9

Best Known (62−52, 62, s)-Nets in Base 9

(62−52, 62, 40)-Net over F₉ — Constructive and digital

Digital (10, 62, 40)-net over F₉, using

t-expansion [i] based on digital (8, 62, 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]

(62−52, 62, 54)-Net over F₉ — Digital

Digital (10, 62, 54)-net over F₉, using

net from sequence [i] based on digital (10, 53)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 10 and N(F) ≥ 54, using
  - a curve from the manYPoints database [i]

(62−52, 62, 201)-Net in Base 9 — Upper bound on s

There is no (10, 62, 202)-net in base 9, because

extracting embedded orthogonal array [i] would yield OA(9⁶², 202, S₉, 52), but
- the linear programming bound shows that MÂ â‰¥ 5149 515178 946146 885556 419173 473662 751859 632749 744986 928844 260049 646556 840073 886060 437471 129369 393947 623622 643157 303500 390025 / 32803 980798 934262 642141 342689 059208 065156 005796 723893 160657 805409 > 9⁶² [i]