Best Known (115, 115+50, s)-Nets in Base 2
(115, 115+50, 84)-Net over F2 — Constructive and digital
Digital (115, 165, 84)-net over F2, using
- trace code for nets [i] based on digital (5, 55, 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
(115, 115+50, 86)-Net in Base 2 — Constructive
(115, 165, 86)-net in base 2, using
- 5 times m-reduction [i] based on (115, 170, 86)-net in base 2, using
- trace code for nets [i] based on (30, 85, 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, 85, 43)-net in base 4, using
(115, 115+50, 149)-Net over F2 — Digital
Digital (115, 165, 149)-net over F2, using
(115, 115+50, 950)-Net in Base 2 — Upper bound on s
There is no (115, 165, 951)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 46 930870 463101 168525 143147 163557 420299 015225 109920 > 2165 [i]