MinT - Best Known (51−32, 51, s)-Nets in Base 3

Best Known (51−32, 51, s)-Nets in Base 3

(51−32, 51, 28)-Net over F₃ — Constructive and digital

Digital (19, 51, 28)-net over F₃, using

t-expansion [i] based on digital (15, 51, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(51−32, 51, 32)-Net over F₃ — Digital

Digital (19, 51, 32)-net over F₃, using

net from sequence [i] based on digital (19, 31)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 19 and N(F) ≥ 32, using
  - a curve from the manYPoints database [i]

(51−32, 51, 90)-Net in Base 3 — Upper bound on s

There is no (19, 51, 91)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵¹, 91, S₃, 32), but
- the linear programming bound shows that MÂ â‰¥ 3 796003 121606 659684 644081 485270 254802 809922 702083 145243 272087 278428 845740 570091 586803 340207 313946 354006 591960 625547 / 1 756668 470243 430645 991636 297238 233510 101788 678484 940922 765709 380449 381903 813470 038571 507115 > 3⁵¹ [i]