Best Known (24, s)-Sequences in Base 4
(24, 33)-Sequence over F4 — Constructive and digital
Digital (24, 33)-sequence over F4, using
- t-expansion [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
(24, 34)-Sequence in Base 4 — Constructive
(24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(24, 48)-Sequence over F4 — Digital
Digital (24, 48)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 24 and N(F) ≥ 49, using
(24, 84)-Sequence in Base 4 — Upper bound on s
There is no (24, 85)-sequence in base 4, because
- net from sequence [i] would yield (24, m, 86)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (24, 254, 86)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4254, 86, S4, 3, 230), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 87150 751544 626881 147231 162488 337999 828615 877833 850556 955203 149384 191466 195478 055349 212182 938084 872279 985207 078212 159330 549400 238277 652704 651818 718539 546624 / 77 > 4254 [i]
- extracting embedded OOA [i] would yield OOA(4254, 86, S4, 3, 230), but
- m-reduction [i] would yield (24, 254, 86)-net in base 4, but