Best Known (45, 45+52, s)-Nets in Base 16
(45, 45+52, 225)-Net over F16 — Constructive and digital
Digital (45, 97, 225)-net over F16, using
- t-expansion [i] based on digital (40, 97, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
(45, 45+52, 247)-Net over F16 — Digital
Digital (45, 97, 247)-net over F16, using
(45, 45+52, 257)-Net in Base 16
(45, 97, 257)-net in base 16, using
- 2 times m-reduction [i] based on (45, 99, 257)-net in base 16, using
- base change [i] based on digital (12, 66, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 66, 257)-net over F64, using
(45, 45+52, 21837)-Net in Base 16 — Upper bound on s
There is no (45, 97, 21838)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 630 440428 703180 927883 205007 848572 689675 350319 605119 588942 958083 829913 755805 825241 665153 402680 075268 146250 485483 108696 > 1697 [i]