MinT - Best Known (20, ∞, s)-Nets in Base 3

Best Known (20, ∞, s)-Nets in Base 3

(20, ∞, 28)-Net over F₃ — Constructive and digital

Digital (20, m, 28)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (20, 27)-sequence over F₃, using
- t-expansion [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]

(20, ∞, 32)-Net over F₃ — Digital

Digital (20, m, 32)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (20, 31)-sequence over F₃, using
- t-expansion [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]

(20, ∞, 50)-Net in Base 3 — Upper bound on s

There is no (20, m, 51)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (20, 148, 51)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁴⁸, 51, S₃, 3, 128), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1 849942 425175 634864 623503 912258 483220 932365 501948 614869 075922 026508 741245 / 43 > 3¹⁴⁸ [i]