Best Known (177−77, 177, s)-Nets in Base 2
(177−77, 177, 55)-Net over F2 — Constructive and digital
Digital (100, 177, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 6 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(177−77, 177, 69)-Net over F2 — Digital
Digital (100, 177, 69)-net over F2, using
(177−77, 177, 294)-Net in Base 2 — Upper bound on s
There is no (100, 177, 295)-net in base 2, because
- 1 times m-reduction [i] would yield (100, 176, 295)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2176, 295, S2, 76), but
- 4 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
- 4 times code embedding in larger space [i] would yield OA(2180, 299, S2, 76), but
- extracting embedded orthogonal array [i] would yield OA(2176, 295, S2, 76), but