Best Known (31, 67, s)-Nets in Base 16
(31, 67, 130)-Net over F16 — Constructive and digital
Digital (31, 67, 130)-net over F16, using
- 2 times m-reduction [i] based on digital (31, 69, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 25, 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 (6, 44, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 25, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(31, 67, 177)-Net in Base 16 — Constructive
(31, 67, 177)-net in base 16, using
- 5 times m-reduction [i] based on (31, 72, 177)-net in base 16, using
- base change [i] based on digital (7, 48, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- base change [i] based on digital (7, 48, 177)-net over F64, using
(31, 67, 183)-Net over F16 — Digital
Digital (31, 67, 183)-net over F16, using
(31, 67, 15267)-Net in Base 16 — Upper bound on s
There is no (31, 67, 15268)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 474 618243 321034 662678 399805 311783 347740 317916 138744 395725 821331 161040 480857 537786 > 1667 [i]