Best Known (114, 205, s)-Nets in Base 2
(114, 205, 59)-Net over F2 — Constructive and digital
Digital (114, 205, 59)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (15, 60, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- digital (54, 145, 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 (15, 60, 17)-net over F2, using
(114, 205, 74)-Net over F2 — Digital
Digital (114, 205, 74)-net over F2, using
(114, 205, 294)-Net in Base 2 — Upper bound on s
There is no (114, 205, 295)-net in base 2, because
- 1 times m-reduction [i] would yield (114, 204, 295)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2204, 295, S2, 90), but
- 4 times code embedding in larger space [i] would yield OA(2208, 299, S2, 90), but
- adding a parity check bit [i] would yield OA(2209, 300, S2, 91), but
- the linear programming bound shows that M ≥ 437987 836379 661851 428112 482969 460104 960459 291237 979833 080590 515802 667419 590325 215760 903409 709975 863296 / 433 753365 263741 276278 643266 060465 678125 > 2209 [i]
- adding a parity check bit [i] would yield OA(2209, 300, S2, 91), but
- 4 times code embedding in larger space [i] would yield OA(2208, 299, S2, 90), but
- extracting embedded orthogonal array [i] would yield OA(2204, 295, S2, 90), but