Best Known (25, 25+114, s)-Nets in Base 3
(25, 25+114, 32)-Net over F3 — Constructive and digital
Digital (25, 139, 32)-net over F3, using
- t-expansion [i] based on digital (21, 139, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
(25, 25+114, 36)-Net over F3 — Digital
Digital (25, 139, 36)-net over F3, using
- net from sequence [i] based on digital (25, 35)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 25 and N(F) ≥ 36, using
(25, 25+114, 65)-Net in Base 3 — Upper bound on s
There is no (25, 139, 66)-net in base 3, because
- 11 times m-reduction [i] would yield (25, 128, 66)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3128, 66, S3, 2, 103), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 318 334983 598941 745631 063567 258138 003973 311712 991447 709945 617947 / 26 > 3128 [i]
- extracting embedded OOA [i] would yield OOA(3128, 66, S3, 2, 103), but