Best Known (131, 197, s)-Nets in Base 2
(131, 197, 76)-Net over F2 — Constructive and digital
Digital (131, 197, 76)-net over F2, using
- t-expansion [i] based on digital (130, 197, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (43, 76, 34)-net over F2, using
- trace code for nets [i] based on digital (5, 38, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- trace code for nets [i] based on digital (5, 38, 17)-net over F4, using
- digital (54, 121, 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 (43, 76, 34)-net over F2, using
- (u, u+v)-construction [i] based on
(131, 197, 86)-Net in Base 2 — Constructive
(131, 197, 86)-net in base 2, using
- 5 times m-reduction [i] based on (131, 202, 86)-net in base 2, using
- trace code for nets [i] based on (30, 101, 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, 101, 43)-net in base 4, using
(131, 197, 136)-Net over F2 — Digital
Digital (131, 197, 136)-net over F2, using
(131, 197, 777)-Net in Base 2 — Upper bound on s
There is no (131, 197, 778)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 207324 004627 039510 193993 205250 982777 148675 844817 224050 432408 > 2197 [i]