Best Known (151, 151+95, s)-Nets in Base 2
(151, 151+95, 77)-Net over F2 — Constructive and digital
Digital (151, 246, 77)-net over F2, using
- 3 times m-reduction [i] based on digital (151, 249, 77)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (48, 97, 35)-net over F2, using
- net from sequence [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]
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- digital (54, 152, 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 (48, 97, 35)-net over F2, using
- (u, u+v)-construction [i] based on
(151, 151+95, 84)-Net in Base 2 — Constructive
(151, 246, 84)-net in base 2, using
- 2 times m-reduction [i] based on (151, 248, 84)-net in base 2, using
- trace code for nets [i] based on (27, 124, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [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
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- trace code for nets [i] based on (27, 124, 42)-net in base 4, using
(151, 151+95, 119)-Net over F2 — Digital
Digital (151, 246, 119)-net over F2, using
(151, 151+95, 614)-Net in Base 2 — Upper bound on s
There is no (151, 246, 615)-net in base 2, because
- 1 times m-reduction [i] would yield (151, 245, 615)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 59 118782 084840 952438 971007 751274 417504 381523 125232 124466 441603 558141 619024 > 2245 [i]