MinT - Best Known (34, 34+62, s)-Nets in Base 3

Best Known (34, 34+62, s)-Nets in Base 3

(34, 34+62, 38)-Net over F₃ — Constructive and digital

Digital (34, 96, 38)-net over F₃, using

t-expansion [i] based on digital (32, 96, 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]

(34, 34+62, 46)-Net over F₃ — Digital

Digital (34, 96, 46)-net over F₃, using

t-expansion [i] based on digital (33, 96, 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]

(34, 34+62, 114)-Net in Base 3 — Upper bound on s

There is no (34, 96, 115)-net in base 3, because

1 times m-reduction [i] would yield (34, 95, 115)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3⁹⁵, 115, S₃, 61), but
  - the linear programming bound shows that MÂ â‰¥ 2 006292 535356 817630 138598 073619 396427 651126 288096 812860 / 883 421539 > 3⁹⁵ [i]