MinT - Best Known (104−65, 104, s)-Nets in Base 3

Best Known (104−65, 104, s)-Nets in Base 3

(104−65, 104, 42)-Net over F₃ — Constructive and digital

Digital (39, 104, 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]

(104−65, 104, 52)-Net over F₃ — Digital

Digital (39, 104, 52)-net over F₃, using

t-expansion [i] based on digital (37, 104, 52)-net over F₃, using
- net from sequence [i] based on digital (37, 51)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 37 and N(F) ≥ 52, using
    - a curve from the manYPoints database [i]

(104−65, 104, 137)-Net in Base 3 — Upper bound on s

There is no (39, 104, 138)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰⁴, 138, S₃, 65), but
- the linear programming bound shows that MÂ â‰¥ 420399 649231 768818 340701 808544 208183 044355 226631 929768 452307 508474 204697 / 8842 335420 690129 150793 > 3¹⁰⁴ [i]