Best Known (229−102, 229, s)-Nets in Base 2
(229−102, 229, 63)-Net over F2 — Constructive and digital
Digital (127, 229, 63)-net over F2, using
- 2 times m-reduction [i] based on digital (127, 231, 63)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (21, 73, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- digital (54, 158, 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 (21, 73, 21)-net over F2, using
- (u, u+v)-construction [i] based on
(229−102, 229, 81)-Net over F2 — Digital
Digital (127, 229, 81)-net over F2, using
- t-expansion [i] based on digital (126, 229, 81)-net over F2, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 126 and N(F) ≥ 81, using
- net from sequence [i] based on digital (126, 80)-sequence over F2, using
(229−102, 229, 292)-Net in Base 2 — Upper bound on s
There is no (127, 229, 293)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2229, 293, S2, 102), but
- the linear programming bound shows that M ≥ 8205 062837 078930 532068 639436 021052 815868 020242 277045 458586 682301 189324 495527 824585 516900 155392 / 7 988981 954712 652237 026475 > 2229 [i]