Best Known (34, s)-Sequences in Base 3
(34, 37)-Sequence over F3 — Constructive and digital
Digital (34, 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
(34, 45)-Sequence over F3 — Digital
Digital (34, 45)-sequence over F3, using
- t-expansion [i] based on digital (33, 45)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 33 and N(F) ≥ 46, using
(34, 78)-Sequence in Base 3 — Upper bound on s
There is no (34, 79)-sequence in base 3, because
- net from sequence [i] would yield (34, m, 80)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (34, 314, 80)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3314, 80, S3, 4, 280), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 241 601901 558808 255480 810106 750959 761525 496530 550725 667504 364320 172551 252618 533199 343528 859969 183401 331740 222554 999779 831546 868843 129811 039523 483186 441561 / 281 > 3314 [i]
- extracting embedded OOA [i] would yield OOA(3314, 80, S3, 4, 280), but
- m-reduction [i] would yield (34, 314, 80)-net in base 3, but