Best Known (36, 36+38, s)-Nets in Base 16
(36, 36+38, 130)-Net over F16 — Constructive and digital
Digital (36, 74, 130)-net over F16, using
- 10 times m-reduction [i] based on digital (36, 84, 130)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 30, 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, 54, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16 (see above)
- digital (6, 30, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(36, 36+38, 192)-Net in Base 16 — Constructive
(36, 74, 192)-net in base 16, using
- 3 times m-reduction [i] based on (36, 77, 192)-net in base 16, using
- base change [i] based on digital (3, 44, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 44, 192)-net over F128, using
(36, 36+38, 248)-Net over F16 — Digital
Digital (36, 74, 248)-net over F16, using
(36, 36+38, 25863)-Net in Base 16 — Upper bound on s
There is no (36, 74, 25864)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 127388 995184 382820 332066 251660 766191 943758 697990 774531 669968 205629 991652 773402 813106 653616 > 1674 [i]