Best Known (153, 153+90, s)-Nets in Base 2
(153, 153+90, 84)-Net over F2 — Constructive and digital
Digital (153, 243, 84)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (54, 99, 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, 144, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2 (see above)
- digital (54, 99, 42)-net over F2, using
(153, 153+90, 86)-Net in Base 2 — Constructive
(153, 243, 86)-net in base 2, using
- 3 times m-reduction [i] based on (153, 246, 86)-net in base 2, using
- trace code for nets [i] based on (30, 123, 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, 123, 43)-net in base 4, using
(153, 153+90, 130)-Net over F2 — Digital
Digital (153, 243, 130)-net over F2, using
(153, 153+90, 679)-Net in Base 2 — Upper bound on s
There is no (153, 243, 680)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 14 210923 120818 181094 892090 907748 926328 524423 951383 199619 453513 040175 481904 > 2243 [i]