MinT - Best Known (3, 3+12, s)-Nets in Base 3

Best Known (3, 3+12, s)-Nets in Base 3

(3, 3+12, 10)-Net over F₃ — Constructive and digital

Digital (3, 15, 10)-net over F₃, using

net from sequence [i] based on digital (3, 9)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
  - an explicitly constructive algebraic function field [i]

(3, 3+12, 13)-Net in Base 3 — Upper bound on s

There is no (3, 15, 14)-net in base 3, because

extracting embedded OOA [i] would yield OOA(3¹⁵, 14, S₃, 2, 12), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 473 513931 / 29 > 3¹⁵ [i]