MinT - Best Known (7, 7+21, s)-Nets in Base 3

Best Known (7, 7+21, s)-Nets in Base 3

(7, 7+21, 16)-Net over F₃ — Constructive and digital

Digital (7, 28, 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]

(7, 7+21, 24)-Net in Base 3 — Upper bound on s

There is no (7, 28, 25)-net in base 3, because

extracting embedded OOA [i] would yield OOA(3²⁸, 25, S₃, 2, 21), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 705 791411 666019 / 25 > 3²⁸ [i]