MinT - Best Known (17, 17+34, s)-Nets in Base 3

Best Known (17, 17+34, s)-Nets in Base 3

(17, 17+34, 28)-Net over F₃ — Constructive and digital

Digital (17, 51, 28)-net over F₃, using

t-expansion [i] based on digital (15, 51, 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]

(17, 17+34, 64)-Net in Base 3 — Upper bound on s

There is no (17, 51, 65)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵¹, 65, S₃, 34), but
- the linear programming bound shows that MÂ â‰¥ 342 054256 122719 546156 841781 498869 / 115 101637 > 3⁵¹ [i]