Best Known (5, 71, s)-Nets in Base 16
(5, 71, 49)-Net over F16 — Constructive and digital
Digital (5, 71, 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
(5, 71, 158)-Net over F16 — Upper bound on s (digital)
There is no digital (5, 71, 159)-net over F16, because
- 2 times m-reduction [i] would yield digital (5, 69, 159)-net over F16, but
- 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
- extracting embedded orthogonal array [i] would yield linear OA(1669, 159, F16, 64) (dual of [159, 90, 65]-code), but
(5, 71, 183)-Net in Base 16 — Upper bound on s
There is no (5, 71, 184)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1671, 184, S16, 66), but
- the linear programming bound shows that M ≥ 736 115296 179792 197406 603832 460392 758683 771472 138505 152276 194264 299873 685131 262688 641541 821786 805799 322346 112582 861954 482176 / 22 908652 434206 366957 779935 808052 259965 > 1671 [i]