Best Known (25, 25+40, s)-Nets in Base 16
(25, 25+40, 71)-Net over F16 — Constructive and digital
Digital (25, 65, 71)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 22, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (3, 43, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (2, 22, 33)-net over F16, using
(25, 25+40, 120)-Net in Base 16 — Constructive
(25, 65, 120)-net in base 16, using
- 5 times m-reduction [i] based on (25, 70, 120)-net in base 16, using
- base change [i] based on digital (11, 56, 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, 56, 120)-net over F32, using
(25, 25+40, 144)-Net over F16 — Digital
Digital (25, 65, 144)-net over F16, using
- net from sequence [i] based on digital (25, 143)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 25 and N(F) ≥ 144, using
(25, 25+40, 4524)-Net in Base 16 — Upper bound on s
There is no (25, 65, 4525)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 1 857075 733965 190378 784892 401903 882058 968948 612219 819488 229293 579517 613614 548126 > 1665 [i]