Best Known (7, s)-Sequences in Base 16
(7, 64)-Sequence over F16 — Constructive and digital
Digital (7, 64)-sequence over F16, using
- t-expansion [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
(7, 118)-Sequence in Base 16 — Upper bound on s
There is no (7, 119)-sequence in base 16, because
- net from sequence [i] would yield (7, m, 120)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (7, 111, 120)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16111, 120, S16, 104), but
- the linear programming bound shows that M ≥ 92086 954283 537596 660104 192126 770459 664696 363604 028357 116797 528075 544556 954927 352946 662893 970276 794850 999821 883009 523266 007059 187150 407449 182208 / 1974 452051 > 16111 [i]
- extracting embedded orthogonal array [i] would yield OA(16111, 120, S16, 104), but
- m-reduction [i] would yield (7, 111, 120)-net in base 16, but