MinT - Best Known (50, 50+197, s)-Nets in Base 3

Best Known (50, 50+197, s)-Nets in Base 3

(50, 50+197, 48)-Net over F₃ — Constructive and digital

Digital (50, 247, 48)-net over F₃, using

t-expansion [i] based on digital (45, 247, 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]

(50, 50+197, 64)-Net over F₃ — Digital

Digital (50, 247, 64)-net over F₃, using

t-expansion [i] based on digital (49, 247, 64)-net over F₃, using
- net from sequence [i] based on digital (49, 63)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
    - a curve from the manYPoints database [i]

(50, 50+197, 123)-Net in Base 3 — Upper bound on s

There is no (50, 247, 124)-net in base 3, because

4 times m-reduction [i] would yield (50, 243, 124)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3²⁴³, 124, S₃, 2, 193), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 11770 601735 604729 357392 994529 091204 179090 149774 638786 261545 904624 128780 557652 664392 369199 237422 277220 766792 455464 859645 / 97 > 3²⁴³ [i]