Best Known (252−97, 252, s)-Nets in Base 2
(252−97, 252, 78)-Net over F2 — Constructive and digital
Digital (155, 252, 78)-net over F2, using
- 3 times m-reduction [i] based on digital (155, 255, 78)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (51, 101, 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, 154, 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, 101, 36)-net over F2, using
- (u, u+v)-construction [i] based on
(252−97, 252, 84)-Net in Base 2 — Constructive
(155, 252, 84)-net in base 2, using
- 4 times m-reduction [i] based on (155, 256, 84)-net in base 2, using
- trace code for nets [i] based on (27, 128, 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, 128, 42)-net in base 4, using
(252−97, 252, 123)-Net over F2 — Digital
Digital (155, 252, 123)-net over F2, using
(252−97, 252, 634)-Net in Base 2 — Upper bound on s
There is no (155, 252, 635)-net in base 2, because
- 1 times m-reduction [i] would yield (155, 251, 635)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3717 155202 171421 780009 237192 231846 325371 849926 903647 531817 353138 735655 637281 > 2251 [i]