Best Known (124, 188, s)-Nets in Base 2
(124, 188, 70)-Net over F2 — Constructive and digital
Digital (124, 188, 70)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (38, 70, 28)-net over F2, using
- trace code for nets [i] based on digital (3, 35, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- trace code for nets [i] based on digital (3, 35, 14)-net over F4, 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 (38, 70, 28)-net over F2, using
(124, 188, 86)-Net in Base 2 — Constructive
(124, 188, 86)-net in base 2, using
- trace code for nets [i] based on (30, 94, 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
(124, 188, 127)-Net over F2 — Digital
Digital (124, 188, 127)-net over F2, using
(124, 188, 704)-Net in Base 2 — Upper bound on s
There is no (124, 188, 705)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 401 322490 667950 540275 537467 784150 387368 429564 300311 469810 > 2188 [i]