Best Known (17, 17+23, s)-Nets in Base 16
(17, 17+23, 82)-Net over F16 — Constructive and digital
Digital (17, 40, 82)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 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, 29, 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, 11, 17)-net over F16, using
(17, 17+23, 104)-Net in Base 16 — Constructive
(17, 40, 104)-net in base 16, using
- base change [i] based on digital (9, 32, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
(17, 17+23, 112)-Net over F16 — Digital
Digital (17, 40, 112)-net over F16, using
- net from sequence [i] based on digital (17, 111)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 17 and N(F) ≥ 112, using
(17, 17+23, 113)-Net in Base 16
(17, 40, 113)-net in base 16, using
- 2 times m-reduction [i] based on (17, 42, 113)-net in base 16, using
- base change [i] based on digital (3, 28, 113)-net over F64, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 113, using
- net from sequence [i] based on digital (3, 112)-sequence over F64, using
- base change [i] based on digital (3, 28, 113)-net over F64, using
(17, 17+23, 6076)-Net in Base 16 — Upper bound on s
There is no (17, 40, 6077)-net in base 16, because
- 1 times m-reduction [i] would yield (17, 39, 6077)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 91397 335106 053893 322397 513747 175561 898190 582956 > 1639 [i]