Best Known (167−71, 167, s)-Nets in Base 2
(167−71, 167, 56)-Net over F2 — Constructive and digital
Digital (96, 167, 56)-net over F2, using
- 1 times m-reduction [i] based on digital (96, 168, 56)-net over F2, using
- trace code for nets [i] based on digital (12, 84, 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, 84, 28)-net over F4, using
(167−71, 167, 69)-Net over F2 — Digital
Digital (96, 167, 69)-net over F2, using
(167−71, 167, 296)-Net in Base 2 — Upper bound on s
There is no (96, 167, 297)-net in base 2, because
- 1 times m-reduction [i] would yield (96, 166, 297)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2166, 297, S2, 70), but
- 2 times code embedding in larger space [i] would yield OA(2168, 299, S2, 70), but
- adding a parity check bit [i] would yield OA(2169, 300, S2, 71), but
- the linear programming bound shows that M ≥ 5 732185 258643 572537 160787 217827 068490 646634 529662 857763 729696 200690 409592 323211 348143 834610 774502 523043 321848 376446 554440 040465 777554 424423 342327 267888 544064 873937 121845 968889 047522 308075 290624 / 7081 736815 532100 923642 349512 429167 715967 827950 147676 375948 182684 180755 163868 731084 610661 157767 128599 722536 496950 125352 041870 828167 670228 933175 > 2169 [i]
- adding a parity check bit [i] would yield OA(2169, 300, S2, 71), but
- 2 times code embedding in larger space [i] would yield OA(2168, 299, S2, 70), but
- extracting embedded orthogonal array [i] would yield OA(2166, 297, S2, 70), but