Best Known (215−78, 215, s)-Nets in Base 2
(215−78, 215, 76)-Net over F2 — Constructive and digital
Digital (137, 215, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 78, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- digital (59, 137, 43)-net over F2, using
- net from sequence [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]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- digital (39, 78, 33)-net over F2, using
(215−78, 215, 84)-Net in Base 2 — Constructive
(137, 215, 84)-net in base 2, using
- 5 times m-reduction [i] based on (137, 220, 84)-net in base 2, using
- trace code for nets [i] based on (27, 110, 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, 110, 42)-net in base 4, using
(215−78, 215, 122)-Net over F2 — Digital
Digital (137, 215, 122)-net over F2, using
(215−78, 215, 647)-Net in Base 2 — Upper bound on s
There is no (137, 215, 648)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 55399 578548 114811 499848 821486 710112 369765 972316 821023 118749 700308 > 2215 [i]