Best Known (256−98, 256, s)-Nets in Base 2
(256−98, 256, 84)-Net over F2 — Constructive and digital
Digital (158, 256, 84)-net over F2, using
- 2 times m-reduction [i] based on digital (158, 258, 84)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (54, 104, 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 (54, 154, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2 (see above)
- digital (54, 104, 42)-net over F2, using
- (u, u+v)-construction [i] based on
(256−98, 256, 86)-Net in Base 2 — Constructive
(158, 256, 86)-net in base 2, using
- trace code for nets [i] based on (30, 128, 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
(256−98, 256, 126)-Net over F2 — Digital
Digital (158, 256, 126)-net over F2, using
(256−98, 256, 644)-Net in Base 2 — Upper bound on s
There is no (158, 256, 645)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 117466 060290 398584 088039 468113 289537 095459 103339 491303 522767 623268 417976 983984 > 2256 [i]