MinT - Best Known (93−59, 93, s)-Nets in Base 3

Best Known (93−59, 93, s)-Nets in Base 3

(93−59, 93, 38)-Net over F₃ — Constructive and digital

Digital (34, 93, 38)-net over F₃, using

t-expansion [i] based on digital (32, 93, 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]

(93−59, 93, 46)-Net over F₃ — Digital

Digital (34, 93, 46)-net over F₃, using

t-expansion [i] based on digital (33, 93, 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]

(93−59, 93, 118)-Net in Base 3 — Upper bound on s

There is no (34, 93, 119)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹³, 119, S₃, 59), but
- the linear programming bound shows that MÂ â‰¥ 1 414037 507073 505742 880079 653115 871460 807495 392949 658535 835441 / 5182 274908 774040 > 3⁹³ [i]