Best Known (132, 216, s)-Nets in Base 2
(132, 216, 69)-Net over F2 — Constructive and digital
Digital (132, 216, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 81, 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 (51, 135, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 3 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (51, 35)-sequence over F2, using
- digital (39, 81, 33)-net over F2, using
(132, 216, 70)-Net in Base 2 — Constructive
(132, 216, 70)-net in base 2, using
- trace code for nets [i] based on (24, 108, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
(132, 216, 105)-Net over F2 — Digital
Digital (132, 216, 105)-net over F2, using
(132, 216, 523)-Net in Base 2 — Upper bound on s
There is no (132, 216, 524)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 106992 431731 034125 892103 687773 864186 640937 291456 299309 256949 297808 > 2216 [i]