MinT - Best Known (21, 21+38, s)-Nets in Base 3

Best Known (21, 21+38, s)-Nets in Base 3

(21, 21+38, 32)-Net over F₃ — Constructive and digital

Digital (21, 59, 32)-net over F₃, using

net from sequence [i] based on digital (21, 31)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(21, 21+38, 82)-Net in Base 3 — Upper bound on s

There is no (21, 59, 83)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵⁹, 83, S₃, 38), but
- the linear programming bound shows that MÂ â‰¥ 325 626781 031292 288709 976539 068217 532079 726399 / 18937 606422 109375 > 3⁵⁹ [i]