Best Known (21, s)-Sequences in Base 4
(21, 33)-Sequence over F4 — Constructive and digital
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]
(21, 43)-Sequence over F4 — Digital
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
(21, 74)-Sequence in Base 4 — Upper bound on s
There is no (21, 75)-sequence in base 4, because
- net from sequence [i] would yield (21, m, 76)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (21, 224, 76)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4224, 76, S4, 3, 203), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 14536 774485 912137 810986 476157 760090 687072 827213 746361 205629 803983 612785 762267 958466 523821 014275 271311 215250 432125 323558 670692 032572 293120 / 17 > 4224 [i]
- extracting embedded OOA [i] would yield OOA(4224, 76, S4, 3, 203), but
- m-reduction [i] would yield (21, 224, 76)-net in base 4, but