Best Known (154−47, 154, s)-Nets in Base 2
(154−47, 154, 76)-Net over F2 — Constructive and digital
Digital (107, 154, 76)-net over F2, using
- 21 times duplication [i] based on digital (106, 153, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (6, 29, 10)-net over F2, using
- net from sequence [i] based on digital (6, 9)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 6 and N(F) ≥ 10, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (6, 9)-sequence over F2, using
- digital (77, 124, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 62, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- trace code for nets [i] based on digital (15, 62, 33)-net over F4, using
- digital (6, 29, 10)-net over F2, using
- (u, u+v)-construction [i] based on
(154−47, 154, 86)-Net in Base 2 — Constructive
(107, 154, 86)-net in base 2, using
- trace code for nets [i] based on (30, 77, 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
(154−47, 154, 138)-Net over F2 — Digital
Digital (107, 154, 138)-net over F2, using
(154−47, 154, 914)-Net in Base 2 — Upper bound on s
There is no (107, 154, 915)-net in base 2, because
- 1 times m-reduction [i] would yield (107, 153, 915)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 11452 159381 254558 285680 942664 984201 888022 432224 > 2153 [i]