Best Known (38, 38+209, s)-Nets in Base 3
(38, 38+209, 38)-Net over F3 — Constructive and digital
Digital (38, 247, 38)-net over F3, using
- t-expansion [i] based on digital (32, 247, 38)-net over F3, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 32 and N(F) ≥ 38, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
(38, 38+209, 52)-Net over F3 — Digital
Digital (38, 247, 52)-net over F3, using
- t-expansion [i] based on digital (37, 247, 52)-net over F3, using
- net from sequence [i] based on digital (37, 51)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 37 and N(F) ≥ 52, using
- net from sequence [i] based on digital (37, 51)-sequence over F3, using
(38, 38+209, 95)-Net in Base 3 — Upper bound on s
There is no (38, 247, 96)-net in base 3, because
- 60 times m-reduction [i] would yield (38, 187, 96)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3187, 96, S3, 2, 149), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 498196 224760 364601 242719 132174 628305 800834 098010 033971 355568 455673 974002 968757 862019 419449 / 25 > 3187 [i]
- extracting embedded OOA [i] would yield OOA(3187, 96, S3, 2, 149), but