Best Known (25, s)-Sequences in Base 5
(25, 50)-Sequence over F5 — Constructive and digital
Digital (25, 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
(25, 54)-Sequence over F5 — Digital
Digital (25, 54)-sequence over F5, using
- t-expansion [i] based on digital (23, 54)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 23 and N(F) ≥ 55, using
(25, 113)-Sequence in Base 5 — Upper bound on s
There is no (25, 114)-sequence in base 5, because
- net from sequence [i] would yield (25, m, 115)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (25, 341, 115)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5341, 115, S5, 3, 316), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7 255291 057944 128305 080657 289047 574449 645913 053074 405564 353826 153300 402474 017381 124892 980607 510857 610077 822122 360284 358895 931170 756685 031135 077416 901528 582102 320157 336859 916207 573206 013739 441572 340410 115116 160483 239582 390524 446964 263916 015625 / 317 > 5341 [i]
- extracting embedded OOA [i] would yield OOA(5341, 115, S5, 3, 316), but
- m-reduction [i] would yield (25, 341, 115)-net in base 5, but