MinT - Best Known (53−33, 53, s)-Nets in Base 3

Best Known (53−33, 53, s)-Nets in Base 3

(53−33, 53, 28)-Net over F₃ — Constructive and digital

Digital (20, 53, 28)-net over F₃, using

t-expansion [i] based on digital (15, 53, 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]

(53−33, 53, 32)-Net over F₃ — Digital

Digital (20, 53, 32)-net over F₃, using

t-expansion [i] based on digital (19, 53, 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]

(53−33, 53, 97)-Net in Base 3 — Upper bound on s

There is no (20, 53, 98)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵³, 98, S₃, 33), but
- the linear programming bound shows that MÂ â‰¥ 70405 986787 631825 456516 749181 938054 391496 023445 621407 247393 974860 100167 193867 925850 156399 787754 027088 012405 632448 512652 067196 819333 / 3435 057828 133240 896934 525314 441640 529877 282946 429987 863449 445479 386348 848486 854894 335014 985183 953870 063104 > 3⁵³ [i]