Best Known (111, 157, s)-Nets in Base 2
(111, 157, 84)-Net over F2 — Constructive and digital
Digital (111, 157, 84)-net over F2, using
- 2 times m-reduction [i] based on digital (111, 159, 84)-net over F2, using
- trace code for nets [i] based on digital (5, 53, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- trace code for nets [i] based on digital (5, 53, 28)-net over F8, using
(111, 157, 86)-Net in Base 2 — Constructive
(111, 157, 86)-net in base 2, using
- 5 times m-reduction [i] based on (111, 162, 86)-net in base 2, using
- trace code for nets [i] based on (30, 81, 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, 81, 43)-net in base 4, using
(111, 157, 154)-Net over F2 — Digital
Digital (111, 157, 154)-net over F2, using
(111, 157, 1036)-Net in Base 2 — Upper bound on s
There is no (111, 157, 1037)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 185415 563139 653297 771683 339082 147870 450632 931840 > 2157 [i]