Best Known (23, s)-Sequences in Base 4
(23, 33)-Sequence over F4 — Constructive and digital
Digital (23, 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
(23, 44)-Sequence over F4 — Digital
Digital (23, 44)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 23 and N(F) ≥ 45, using
(23, 80)-Sequence in Base 4 — Upper bound on s
There is no (23, 81)-sequence in base 4, because
- net from sequence [i] would yield (23, m, 82)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (23, 242, 82)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4242, 82, S4, 3, 219), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2896 982654 693240 790722 122229 248058 331734 699076 393093 227997 297658 532344 973624 742495 471644 063642 920549 236319 392080 665346 046975 721430 379528 764237 283328 / 55 > 4242 [i]
- extracting embedded OOA [i] would yield OOA(4242, 82, S4, 3, 219), but
- m-reduction [i] would yield (23, 242, 82)-net in base 4, but