MinT - Best Known (97−63, 97, s)-Nets in Base 3

Best Known (97−63, 97, s)-Nets in Base 3

(97−63, 97, 38)-Net over F₃ — Constructive and digital

Digital (34, 97, 38)-net over F₃, using

t-expansion [i] based on digital (32, 97, 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]

(97−63, 97, 46)-Net over F₃ — Digital

Digital (34, 97, 46)-net over F₃, using

t-expansion [i] based on digital (33, 97, 46)-net over F₃, using
- net from sequence [i] based on digital (33, 45)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 33 and N(F) ≥ 46, using
    - a curve from the manYPoints database [i]

(97−63, 97, 112)-Net in Base 3 — Upper bound on s

There is no (34, 97, 113)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁷, 113, S₃, 63), but
- the linear programming bound shows that MÂ â‰¥ 203 778832 248021 875784 169145 873391 215846 198657 212886 451207 / 9419 125760 > 3⁹⁷ [i]