MinT - Best Known (38, 38+∞, s)-Nets in Base 3

Best Known (38, 38+∞, s)-Nets in Base 3

(38, 38+∞, 38)-Net over F₃ — Constructive and digital

Digital (38, m, 38)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (38, 37)-sequence over F₃, using
- t-expansion [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]

(38, 38+∞, 52)-Net over F₃ — Digital

Digital (38, m, 52)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (38, 51)-sequence over F₃, using
- t-expansion [i] based on digital (37, 51)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 37 and N(F) ≥ 52, using
    - a curve from the manYPoints database [i]

(38, 38+∞, 87)-Net in Base 3 — Upper bound on s

There is no (38, m, 88)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (38, 346, 88)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3³⁴⁶, 88, S₃, 4, 308), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 134671 938588 441224 113431 736827 290363 245597 051186 402233 094311 094053 748600 754444 196567 509079 338081 106678 435003 151014 332077 567079 051883 911111 653043 899025 362948 629563 002119 / 103 > 3³⁴⁶ [i]