Best Known (30, s)-Sequences in Base 5
(30, 50)-Sequence over F5 — Constructive and digital
Digital (30, 50)-sequence over F5, using
- t-expansion [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
(30, 57)-Sequence over F5 — Digital
Digital (30, 57)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 30 and N(F) ≥ 58, using
(30, 134)-Sequence in Base 5 — Upper bound on s
There is no (30, 135)-sequence in base 5, because
- net from sequence [i] would yield (30, m, 136)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (30, 404, 136)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5404, 136, S5, 3, 374), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8 810146 606282 199070 661019 690726 450453 222248 661910 999218 984660 691558 547191 922235 570062 602082 980208 207965 830909 204686 413652 068652 807707 596967 813273 565236 372369 305542 048490 457576 229932 887298 972565 556591 311395 684993 960412 389619 867154 126506 994071 647838 051575 263307 313434 779644 012451 171875 / 3 > 5404 [i]
- extracting embedded OOA [i] would yield OOA(5404, 136, S5, 3, 374), but
- m-reduction [i] would yield (30, 404, 136)-net in base 5, but