Best Known (22, s)-Sequences in Base 4
(22, 33)-Sequence over F4 — Constructive and digital
Digital (22, 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
(22, 43)-Sequence over F4 — Digital
Digital (22, 43)-sequence over F4, using
- t-expansion [i] based on digital (21, 43)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 44, using
(22, 77)-Sequence in Base 4 — Upper bound on s
There is no (22, 78)-sequence in base 4, because
- net from sequence [i] would yield (22, m, 79)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (22, 233, 79)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4233, 79, S4, 3, 211), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11241 648221 963106 790253 554477 404590 578562 456690 504962 030071 427039 666560 827048 716527 532840 581100 221331 691271 297373 229415 944301 181950 562062 565376 / 53 > 4233 [i]
- extracting embedded OOA [i] would yield OOA(4233, 79, S4, 3, 211), but
- m-reduction [i] would yield (22, 233, 79)-net in base 4, but