Best Known (20, s)-Sequences in Base 4
(20, 32)-Sequence over F4 — Constructive and digital
Digital (20, 32)-sequence over F4, using
- t-expansion [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
(20, 40)-Sequence over F4 — Digital
Digital (20, 40)-sequence over F4, using
- t-expansion [i] based on digital (18, 40)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 18 and N(F) ≥ 41, using
(20, 71)-Sequence in Base 4 — Upper bound on s
There is no (20, 72)-sequence in base 4, because
- net from sequence [i] would yield (20, m, 73)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (20, 215, 73)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4215, 73, S4, 3, 195), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 169132 851341 369706 434283 265232 728105 909622 661597 924811 085399 254417 491899 776143 163005 438438 772352 514263 940863 868645 617881 567423 627264 / 49 > 4215 [i]
- extracting embedded OOA [i] would yield OOA(4215, 73, S4, 3, 195), but
- m-reduction [i] would yield (20, 215, 73)-net in base 4, but