Best Known (69−64, 69, s)-Nets in Base 16
(69−64, 69, 49)-Net over F16 — Constructive and digital
Digital (5, 69, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
(69−64, 69, 158)-Net over F16 — Upper bound on s (digital)
There is no digital (5, 69, 159)-net over F16, because
- extracting embedded orthogonal array [i] would yield linear OA(1669, 159, F16, 64) (dual of [159, 90, 65]-code), but
- residual code [i] would yield OA(165, 94, S16, 4), but
- the linear programming bound shows that M ≥ 2179 760128 / 2071 > 165 [i]
- residual code [i] would yield OA(165, 94, S16, 4), but
(69−64, 69, 184)-Net in Base 16 — Upper bound on s
There is no (5, 69, 185)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1669, 185, S16, 64), but
- the linear programming bound shows that M ≥ 1 769833 677696 556407 556152 803437 803601 070961 959347 589111 711578 967954 207146 725075 265611 258260 696144 974811 452247 852287 059715 686400 / 14 370256 564545 030682 215311 081095 318206 546329 > 1669 [i]