MinT - Best Known (89−54, 89, s)-Nets in Base 3

Best Known (89−54, 89, s)-Nets in Base 3

(89−54, 89, 38)-Net over F₃ — Constructive and digital

Digital (35, 89, 38)-net over F₃, using

t-expansion [i] based on digital (32, 89, 38)-net over F₃, using
- net from sequence [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(89−54, 89, 47)-Net over F₃ — Digital

Digital (35, 89, 47)-net over F₃, using

net from sequence [i] based on digital (35, 46)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 35 and N(F) ≥ 47, using
  - a curve from the manYPoints database [i]

(89−54, 89, 149)-Net in Base 3 — Upper bound on s

There is no (35, 89, 150)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁸⁹, 150, S₃, 54), but
- the linear programming bound shows that MÂ â‰¥ 406 638533 152708 985119 618498 486589 571200 186839 052282 246272 982332 898830 001122 097445 061272 732533 696742 061554 297174 363928 497403 854544 524477 649557 / 131 738996 510306 938195 039868 448552 927091 091105 069910 361641 190726 466646 196904 396395 349728 920397 360640 > 3⁸⁹ [i]