MinT - Best Known (52−33, 52, s)-Nets in Base 3

Best Known (52−33, 52, s)-Nets in Base 3

(52−33, 52, 28)-Net over F₃ — Constructive and digital

Digital (19, 52, 28)-net over F₃, using

t-expansion [i] based on digital (15, 52, 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]

(52−33, 52, 32)-Net over F₃ — Digital

Digital (19, 52, 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]

(52−33, 52, 84)-Net in Base 3 — Upper bound on s

There is no (19, 52, 85)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵², 85, S₃, 33), but
- the linear programming bound shows that MÂ â‰¥ 860342 754412 435094 906698 858579 674571 922984 984079 / 127652 777684 493779 532100 > 3⁵² [i]