MinT - Best Known (239−193, 239, s)-Nets in Base 3

Best Known (239−193, 239, s)-Nets in Base 3

(239−193, 239, 48)-Net over F₃ — Constructive and digital

Digital (46, 239, 48)-net over F₃, using

t-expansion [i] based on digital (45, 239, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(239−193, 239, 56)-Net over F₃ — Digital

Digital (46, 239, 56)-net over F₃, using

t-expansion [i] based on digital (40, 239, 56)-net over F₃, using
- net from sequence [i] based on digital (40, 55)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
    - a curve from the manYPoints database [i]

(239−193, 239, 114)-Net in Base 3 — Upper bound on s

There is no (46, 239, 115)-net in base 3, because

14 times m-reduction [i] would yield (46, 225, 115)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3²²⁵, 115, S₃, 2, 179), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 675155 121849 745212 129793 196759 870681 725592 001960 937203 444022 441244 641816 765582 369161 757600 591162 976283 304329 / 2 > 3²²⁵ [i]