MinT - Best Known (250−214, 250, s)-Nets in Base 3

Best Known (250−214, 250, s)-Nets in Base 3

(250−214, 250, 38)-Net over F₃ — Constructive and digital

Digital (36, 250, 38)-net over F₃, using

t-expansion [i] based on digital (32, 250, 38)-net over F₃, using
- net from sequence [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]

(250−214, 250, 48)-Net over F₃ — Digital

Digital (36, 250, 48)-net over F₃, using

net from sequence [i] based on digital (36, 47)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 36 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(250−214, 250, 84)-Net in Base 3 — Upper bound on s

There is no (36, 250, 85)-net in base 3, because

extracting embedded OOA [i] would yield OOA(3²⁵⁰, 85, S₃, 3, 214), but
- the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 8 580768 665255 847701 539493 011707 487846 556719 185711 675184 666964 470989 881026 528792 342037 146244 080840 093938 991700 033882 681205 / 43 > 3²⁵⁰ [i]