MinT - Best Known (94−60, 94, s)-Nets in Base 3

Best Known (94−60, 94, s)-Nets in Base 3

(94−60, 94, 38)-Net over F₃ — Constructive and digital

Digital (34, 94, 38)-net over F₃, using

t-expansion [i] based on digital (32, 94, 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]

(94−60, 94, 46)-Net over F₃ — Digital

Digital (34, 94, 46)-net over F₃, using

t-expansion [i] based on digital (33, 94, 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]

(94−60, 94, 116)-Net in Base 3 — Upper bound on s

There is no (34, 94, 117)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁴, 117, S₃, 60), but
- the linear programming bound shows that MÂ â‰¥ 795 363616 931300 955537 593624 992885 518341 910897 108275 590083 / 912553 212835 > 3⁹⁴ [i]