MinT - Best Known (6, 23, s)-Nets in Base 3

Best Known (6, 23, s)-Nets in Base 3

(6, 23, 14)-Net over F₃ — Constructive and digital

Digital (6, 23, 14)-net over F₃, using

net from sequence [i] based on digital (6, 13)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 6 and N(F) ≥ 14, using
  - an explicitly constructive algebraic function field [i]

(6, 23, 23)-Net in Base 3 — Upper bound on s

There is no (6, 23, 24)-net in base 3, because

1 times m-reduction [i] would yield (6, 22, 24)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3²², 24, S₃, 2, 16), but
  - the linear programming bound for OOAs shows that MÂ â‰¥ 6341 390382 607893 / 192185 > 3²² [i]