Best Known (174−76, 174, s)-Nets in Base 2
(174−76, 174, 54)-Net over F2 — Constructive and digital
Digital (98, 174, 54)-net over F2, using
- t-expansion [i] based on digital (95, 174, 54)-net over F2, using
- net from sequence [i] based on digital (95, 53)-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 5 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]
- net from sequence [i] based on digital (95, 53)-sequence over F2, using
(174−76, 174, 67)-Net over F2 — Digital
Digital (98, 174, 67)-net over F2, using
(174−76, 174, 292)-Net in Base 2 — Upper bound on s
There is no (98, 174, 293)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2174, 293, S2, 76), but
- 6 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
- 6 times code embedding in larger space [i] would yield OA(2180, 299, S2, 76), but