MinT - Best Known (4, 4+17, s)-Nets in Base 3

Best Known (4, 4+17, s)-Nets in Base 3

(4, 4+17, 12)-Net over F₃ — Constructive and digital

Digital (4, 21, 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]

(4, 4+17, 15)-Net in Base 3 — Upper bound on s

There is no (4, 21, 16)-net in base 3, because

2 times m-reduction [i] would yield (4, 19, 16)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁹, 16, S₃, 2, 15), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 186090 974883 / 155 > 3¹⁹ [i]