Best Known (111, 111+48, s)-Nets in Base 2
(111, 111+48, 84)-Net over F2 — Constructive and digital
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
(111, 111+48, 86)-Net in Base 2 — Constructive
(111, 159, 86)-net in base 2, using
- 3 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, 111+48, 146)-Net over F2 — Digital
Digital (111, 159, 146)-net over F2, using
(111, 111+48, 932)-Net in Base 2 — Upper bound on s
There is no (111, 159, 933)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 736909 453033 785875 728332 902225 788426 755285 399892 > 2159 [i]