MinT - Best Known (16−12, 16, s)-Nets in Base 3

Best Known (16−12, 16, s)-Nets in Base 3

(16−12, 16, 12)-Net over F₃ — Constructive and digital

Digital (4, 16, 12)-net over F₃, using

net from sequence [i] based on digital (4, 11)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
  - an explicitly constructive algebraic function field [i]

(16−12, 16, 18)-Net in Base 3 — Upper bound on s

There is no (4, 16, 19)-net in base 3, because

extracting embedded OOA [i] would yield OOA(3¹⁶, 19, S₃, 2, 12), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 4 919077 948833 / 105781 > 3¹⁶ [i]