Best Known (60−51, 60, s)-Nets in Base 16
(60−51, 60, 65)-Net over F16 — Constructive and digital
Digital (9, 60, 65)-net over F16, using
- t-expansion [i] based on digital (6, 60, 65)-net over F16, using
- net from sequence [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
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(60−51, 60, 72)-Net over F16 — Digital
Digital (9, 60, 72)-net over F16, using
- net from sequence [i] based on digital (9, 71)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 9 and N(F) ≥ 72, using
(60−51, 60, 457)-Net in Base 16 — Upper bound on s
There is no (9, 60, 458)-net in base 16, because
- 1 times m-reduction [i] would yield (9, 59, 458)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 112259 567199 542488 610490 637968 397052 146223 197960 486968 164485 937564 179876 > 1659 [i]