Best Known (127, 196, s)-Nets in Base 2
(127, 196, 75)-Net over F2 — Constructive and digital
Digital (127, 196, 75)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 73, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- digital (54, 123, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (39, 73, 33)-net over F2, using
(127, 196, 84)-Net in Base 2 — Constructive
(127, 196, 84)-net in base 2, using
- 4 times m-reduction [i] based on (127, 200, 84)-net in base 2, using
- trace code for nets [i] based on (27, 100, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- trace code for nets [i] based on (27, 100, 42)-net in base 4, using
(127, 196, 121)-Net over F2 — Digital
Digital (127, 196, 121)-net over F2, using
(127, 196, 672)-Net in Base 2 — Upper bound on s
There is no (127, 196, 673)-net in base 2, because
- 1 times m-reduction [i] would yield (127, 195, 673)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 52353 535693 100889 433207 139964 584843 968014 914498 630228 921332 > 2195 [i]