MinT - Best Known (49−32, 49, s)-Nets in Base 3

Best Known (49−32, 49, s)-Nets in Base 3

(49−32, 49, 28)-Net over F₃ — Constructive and digital

Digital (17, 49, 28)-net over F₃, using

t-expansion [i] based on digital (15, 49, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(49−32, 49, 68)-Net in Base 3 — Upper bound on s

There is no (17, 49, 69)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴⁹, 69, S₃, 32), but
- the linear programming bound shows that MÂ â‰¥ 216581 757923 721967 421601 778838 750385 / 815783 089121 > 3⁴⁹ [i]