MinT - Best Known (57−36, 57, s)-Nets in Base 3

Best Known (57−36, 57, s)-Nets in Base 3

(57−36, 57, 32)-Net over F₃ — Constructive and digital

Digital (21, 57, 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]

(57−36, 57, 91)-Net in Base 3 — Upper bound on s

There is no (21, 57, 92)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵⁷, 92, S₃, 36), but
- the linear programming bound shows that MÂ â‰¥ 120 721890 049904 553965 455860 898229 550534 869060 685567 / 70191 477994 212742 316032 > 3⁵⁷ [i]