MinT - Best Known (115−74, 115, s)-Nets in Base 3

Best Known (115−74, 115, s)-Nets in Base 3

(115−74, 115, 42)-Net over F₃ — Constructive and digital

Digital (41, 115, 42)-net over F₃, using

t-expansion [i] based on digital (39, 115, 42)-net over F₃, using
- net from sequence [i] based on digital (39, 41)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(115−74, 115, 56)-Net over F₃ — Digital

Digital (41, 115, 56)-net over F₃, using

t-expansion [i] based on digital (40, 115, 56)-net over F₃, using
- net from sequence [i] based on digital (40, 55)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
    - a curve from the manYPoints database [i]

(115−74, 115, 134)-Net in Base 3 — Upper bound on s

There is no (41, 115, 135)-net in base 3, because

1 times m-reduction [i] would yield (41, 114, 135)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹¹⁴, 135, S₃, 73), but
  - the linear programming bound shows that MÂ â‰¥ 648542 683067 666244 515848 653487 718414 242961 385056 317191 888096 533727 / 238076 928719 > 3¹¹⁴ [i]