Best Known (127−51, 127, s)-Nets in Base 2
(127−51, 127, 56)-Net over F2 — Constructive and digital
Digital (76, 127, 56)-net over F2, using
- 1 times m-reduction [i] based on digital (76, 128, 56)-net over F2, using
- trace code for nets [i] based on digital (12, 64, 28)-net over F4, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 12 and N(F) ≥ 28, using
- net from sequence [i] based on digital (12, 27)-sequence over F4, using
- trace code for nets [i] based on digital (12, 64, 28)-net over F4, using
(127−51, 127, 63)-Net over F2 — Digital
Digital (76, 127, 63)-net over F2, using
(127−51, 127, 298)-Net in Base 2 — Upper bound on s
There is no (76, 127, 299)-net in base 2, because
- 1 times m-reduction [i] would yield (76, 126, 299)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2126, 299, S2, 50), but
- adding a parity check bit [i] would yield OA(2127, 300, S2, 51), but
- the linear programming bound shows that M ≥ 68311 280696 217391 499347 177025 200921 455989 917394 449071 732453 854635 557386 567847 593067 186623 764917 500851 072163 823824 407390 333412 501125 857280 / 291 523462 914014 779723 859678 674439 955163 329953 558815 789355 418053 324666 468440 138090 214368 074041 918247 > 2127 [i]
- adding a parity check bit [i] would yield OA(2127, 300, S2, 51), but
- extracting embedded orthogonal array [i] would yield OA(2126, 299, S2, 50), but