Best Known (156−48, 156, s)-Nets in Base 2
(156−48, 156, 76)-Net over F2 — Constructive and digital
Digital (108, 156, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (6, 30, 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 (78, 126, 66)-net over F2, using
- trace code for nets [i] based on digital (15, 63, 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, 63, 33)-net over F4, using
- digital (6, 30, 10)-net over F2, using
(156−48, 156, 86)-Net in Base 2 — Constructive
(108, 156, 86)-net in base 2, using
- trace code for nets [i] based on (30, 78, 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
(156−48, 156, 137)-Net over F2 — Digital
Digital (108, 156, 137)-net over F2, using
(156−48, 156, 852)-Net in Base 2 — Upper bound on s
There is no (108, 156, 853)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 92818 379778 549697 922580 936090 457641 833858 219864 > 2156 [i]