Best Known (167−72, 167, s)-Nets in Base 2
(167−72, 167, 54)-Net over F2 — Constructive and digital
Digital (95, 167, 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]
(167−72, 167, 67)-Net over F2 — Digital
Digital (95, 167, 67)-net over F2, using
(167−72, 167, 293)-Net in Base 2 — Upper bound on s
There is no (95, 167, 294)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2167, 294, S2, 72), but
- 5 times code embedding in larger space [i] would yield OA(2172, 299, S2, 72), but
- adding a parity check bit [i] would yield OA(2173, 300, S2, 73), but
- the linear programming bound shows that M ≥ 584544 688823 027303 992019 163598 045555 622337 400280 994951 338862 689959 811855 040528 082821 117754 420356 767072 183448 423051 141055 104052 613046 921671 348534 995558 126247 662793 381156 267711 356435 604715 864064 / 41 038286 307966 395039 063876 290815 988845 786829 602951 956598 132356 196127 847068 738398 927371 780621 753648 857584 870215 906243 626062 026359 862634 140625 > 2173 [i]
- adding a parity check bit [i] would yield OA(2173, 300, S2, 73), but
- 5 times code embedding in larger space [i] would yield OA(2172, 299, S2, 72), but