Best Known (109, 194, s)-Nets in Base 2
(109, 194, 57)-Net over F2 — Constructive and digital
Digital (109, 194, 57)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (13, 55, 15)-net over F2, using
- net from sequence [i] based on digital (13, 14)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 13 and N(F) ≥ 15, using
- net from sequence [i] based on digital (13, 14)-sequence over F2, using
- digital (54, 139, 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 (13, 55, 15)-net over F2, using
(109, 194, 73)-Net over F2 — Digital
Digital (109, 194, 73)-net over F2, using
(109, 194, 295)-Net in Base 2 — Upper bound on s
There is no (109, 194, 296)-net in base 2, because
- 1 times m-reduction [i] would yield (109, 193, 296)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2193, 296, S2, 84), but
- 3 times code embedding in larger space [i] would yield OA(2196, 299, S2, 84), but
- adding a parity check bit [i] would yield OA(2197, 300, S2, 85), but
- the linear programming bound shows that M ≥ 333445 596634 842101 957662 761369 966680 970228 955880 375209 681209 067512 159971 176505 925710 036206 046927 475988 200870 117376 / 1 055603 696799 631985 996897 950925 994087 362055 971326 408581 > 2197 [i]
- adding a parity check bit [i] would yield OA(2197, 300, S2, 85), but
- 3 times code embedding in larger space [i] would yield OA(2196, 299, S2, 84), but
- extracting embedded orthogonal array [i] would yield OA(2193, 296, S2, 84), but