Best Known (156, 156+101, s)-Nets in Base 2
(156, 156+101, 78)-Net over F2 — Constructive and digital
Digital (156, 257, 78)-net over F2, using
- 1 times m-reduction [i] based on digital (156, 258, 78)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (51, 102, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-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 3 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 (51, 35)-sequence over F2, using
- digital (54, 156, 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 (51, 102, 36)-net over F2, using
- (u, u+v)-construction [i] based on
(156, 156+101, 84)-Net in Base 2 — Constructive
(156, 257, 84)-net in base 2, using
- 1 times m-reduction [i] based on (156, 258, 84)-net in base 2, using
- trace code for nets [i] based on (27, 129, 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, 129, 42)-net in base 4, using
(156, 156+101, 119)-Net over F2 — Digital
Digital (156, 257, 119)-net over F2, using
(156, 156+101, 606)-Net in Base 2 — Upper bound on s
There is no (156, 257, 607)-net in base 2, because
- 1 times m-reduction [i] would yield (156, 256, 607)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 119459 315362 235948 962907 819889 436363 222538 465810 684703 435567 621734 423155 182786 > 2256 [i]