MinT - Best Known (89−82, 89, s)-Nets in Base 3

Best Known (89−82, 89, s)-Nets in Base 3

(89−82, 89, 16)-Net over F₃ — Constructive and digital

Digital (7, 89, 16)-net over F₃, using

net from sequence [i] based on digital (7, 15)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 7 and N(F) ≥ 16, using
  - an explicitly constructive algebraic function field [i]

(89−82, 89, 22)-Net in Base 3 — Upper bound on s

There is no (7, 89, 23)-net in base 3, because

54 times m-reduction [i] would yield (7, 35, 23)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3³⁵, 23, S₃, 2, 28), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 1 050995 602043 303294 963563 814764 130877 / 19 578586 921145 663665 > 3³⁵ [i]