Best Known (122, 122+59, s)-Nets in Base 2
(122, 122+59, 76)-Net over F2 — Constructive and digital
Digital (122, 181, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 68, 34)-net over F2, using
- trace code for nets [i] based on digital (5, 34, 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, 34, 17)-net over F4, using
- digital (54, 113, 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 (39, 68, 34)-net over F2, using
(122, 122+59, 86)-Net in Base 2 — Constructive
(122, 181, 86)-net in base 2, using
- 3 times m-reduction [i] based on (122, 184, 86)-net in base 2, using
- trace code for nets [i] based on (30, 92, 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, 92, 43)-net in base 4, using
(122, 122+59, 135)-Net over F2 — Digital
Digital (122, 181, 135)-net over F2, using
(122, 122+59, 820)-Net in Base 2 — Upper bound on s
There is no (122, 181, 821)-net in base 2, because
- 1 times m-reduction [i] would yield (122, 180, 821)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 579264 299320 425210 561782 292917 010644 409508 347026 380104 > 2180 [i]