Best Known (48, s)-Sequences in Base 5
(48, 81)-Sequence over F5 — Constructive and digital
Digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
(48, 91)-Sequence over F5 — Digital
Digital (48, 91)-sequence over F5, using
- t-expansion [i] based on digital (47, 91)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 47 and N(F) ≥ 92, using
(48, 208)-Sequence in Base 5 — Upper bound on s
There is no (48, 209)-sequence in base 5, because
- net from sequence [i] would yield (48, m, 210)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (48, 626, 210)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5626, 210, S5, 3, 578), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 80 798859 841845 769657 443278 701650 278374 102132 732380 486080 321296 283711 622192 495872 591738 158387 164532 058452 104594 406905 070397 055308 762706 664329 606048 005869 168333 722386 277721 114693 529208 622416 715793 896077 206797 687648 058673 057312 295617 120284 721893 339803 741258 999738 385911 729554 158018 218688 906606 101024 010288 050265 166979 261825 962070 774464 401607 422401 080712 412766 769891 388964 327451 567666 819748 984974 761487 655448 011224 734727 875329 554080 963134 765625 / 193 > 5626 [i]
- extracting embedded OOA [i] would yield OOA(5626, 210, S5, 3, 578), but
- m-reduction [i] would yield (48, 626, 210)-net in base 5, but