Best Known (15, s)-Sequences in Base 7
(15, 22)-Sequence over F7 — Constructive and digital
Digital (15, 22)-sequence over F7, using
(15, 47)-Sequence over F7 — Digital
Digital (15, 47)-sequence over F7, using
- t-expansion [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
(15, 106)-Sequence in Base 7 — Upper bound on s
There is no (15, 107)-sequence in base 7, because
- net from sequence [i] would yield (15, m, 108)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (15, 213, 108)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7213, 108, S7, 2, 198), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 219 959263 521121 203458 445918 825688 631593 444842 427135 365322 015188 309591 612642 274535 896532 994272 053854 562239 434041 618006 652422 484902 485444 974825 620207 788621 610341 301138 150263 852377 538319 / 199 > 7213 [i]
- extracting embedded OOA [i] would yield OOA(7213, 108, S7, 2, 198), but
- m-reduction [i] would yield (15, 213, 108)-net in base 7, but