Best Known (29, 29+32, s)-Nets in Base 16
(29, 29+32, 130)-Net over F16 — Constructive and digital
Digital (29, 61, 130)-net over F16, using
- 2 times m-reduction [i] based on digital (29, 63, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 23, 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, 40, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 23, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(29, 29+32, 177)-Net in Base 16 — Constructive
(29, 61, 177)-net in base 16, using
- 5 times m-reduction [i] based on (29, 66, 177)-net in base 16, using
- base change [i] based on digital (7, 44, 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, 44, 177)-net over F64, using
(29, 29+32, 193)-Net over F16 — Digital
Digital (29, 61, 193)-net over F16, using
(29, 29+32, 17658)-Net in Base 16 — Upper bound on s
There is no (29, 61, 17659)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 28 292279 819123 973944 676842 605877 722198 903671 686049 779724 625498 037318 115661 > 1661 [i]