Best Known (38, s)-Sequences in Base 3
(38, 37)-Sequence over F3 — Constructive and digital
Digital (38, 37)-sequence over F3, using
- t-expansion [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
(38, 51)-Sequence over F3 — Digital
Digital (38, 51)-sequence over F3, using
- t-expansion [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
(38, 86)-Sequence in Base 3 — Upper bound on s
There is no (38, 87)-sequence in base 3, because
- net from sequence [i] would yield (38, m, 88)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (38, 346, 88)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3346, 88, S3, 4, 308), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 134671 938588 441224 113431 736827 290363 245597 051186 402233 094311 094053 748600 754444 196567 509079 338081 106678 435003 151014 332077 567079 051883 911111 653043 899025 362948 629563 002119 / 103 > 3346 [i]
- extracting embedded OOA [i] would yield OOA(3346, 88, S3, 4, 308), but
- m-reduction [i] would yield (38, 346, 88)-net in base 3, but