Best Known (125, 188, s)-Nets in Base 2
(125, 188, 75)-Net over F2 — Constructive and digital
Digital (125, 188, 75)-net over F2, using
- 1 times m-reduction [i] based on digital (125, 189, 75)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 71, 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, 118, 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, 71, 33)-net over F2, using
- (u, u+v)-construction [i] based on
(125, 188, 86)-Net in Base 2 — Constructive
(125, 188, 86)-net in base 2, using
- 2 times m-reduction [i] based on (125, 190, 86)-net in base 2, using
- trace code for nets [i] based on (30, 95, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- trace code for nets [i] based on (30, 95, 43)-net in base 4, using
(125, 188, 131)-Net over F2 — Digital
Digital (125, 188, 131)-net over F2, using
(125, 188, 767)-Net in Base 2 — Upper bound on s
There is no (125, 188, 768)-net in base 2, because
- 1 times m-reduction [i] would yield (125, 187, 768)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 197 343577 213414 322029 026579 215692 834841 880970 052495 933265 > 2187 [i]