Best Known (34, 34+56, s)-Nets in Base 16
(34, 34+56, 82)-Net over F16 — Constructive and digital
Digital (34, 90, 82)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 28, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (6, 62, 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
- digital (0, 28, 17)-net over F16, using
(34, 34+56, 120)-Net in Base 16 — Constructive
(34, 90, 120)-net in base 16, using
- 25 times m-reduction [i] based on (34, 115, 120)-net in base 16, using
- base change [i] based on digital (11, 92, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 92, 120)-net over F32, using
(34, 34+56, 193)-Net over F16 — Digital
Digital (34, 90, 193)-net over F16, using
- t-expansion [i] based on digital (33, 90, 193)-net over F16, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 33 and N(F) ≥ 193, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
(34, 34+56, 5573)-Net in Base 16 — Upper bound on s
There is no (34, 90, 5574)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 358001 649172 252739 780744 760747 663180 012256 016164 017493 201470 188024 235399 771673 595163 022858 717283 951900 120456 > 1690 [i]