Best Known (178−77, 178, s)-Nets in Base 2
(178−77, 178, 56)-Net over F2 — Constructive and digital
Digital (101, 178, 56)-net over F2, using
- trace code for nets [i] based on digital (12, 89, 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
(178−77, 178, 70)-Net over F2 — Digital
Digital (101, 178, 70)-net over F2, using
(178−77, 178, 295)-Net in Base 2 — Upper bound on s
There is no (101, 178, 296)-net in base 2, because
- 1 times m-reduction [i] would yield (101, 177, 296)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2177, 296, S2, 76), but
- 3 times code embedding in larger space [i] would yield OA(2180, 299, S2, 76), but
- adding a parity check bit [i] would yield OA(2181, 300, S2, 77), but
- the linear programming bound shows that M ≥ 1 701534 483732 309366 379627 599831 667953 620265 452247 654243 213636 197092 258809 472732 009400 892048 846161 501132 017233 770139 644607 995756 675072 / 416986 183620 888257 525186 905206 719820 461288 987101 265210 382835 230557 021727 403215 > 2181 [i]
- adding a parity check bit [i] would yield OA(2181, 300, S2, 77), but
- 3 times code embedding in larger space [i] would yield OA(2180, 299, S2, 76), but
- extracting embedded orthogonal array [i] would yield OA(2177, 296, S2, 76), but