Best Known (19, 24, s)-Nets in Base 9
(19, 24, 58418)-Net over F9 — Constructive and digital
Digital (19, 24, 58418)-net over F9, using
- net defined by OOA [i] based on linear OOA(924, 58418, F9, 6, 5) (dual of [(58418, 6), 350484, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(924, 58419, F9, 2, 5) (dual of [(58419, 2), 116814, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(90, 6491, F9, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(90, s, F9, 2, 0) with arbitrarily large s, using
- linear OOA(90, 6491, F9, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
- linear OOA(90, 6491, F9, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
- linear OOA(90, 6491, F9, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code) (see above)
- linear OOA(91, 6491, F9, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(91, s, F9, 2, 1) with arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(91, s, F9, 2, 1) with arbitrarily large s, using
- linear OOA(91, 6491, F9, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code) (see above)
- linear OOA(91, 6491, F9, 2, 1) (dual of [(6491, 2), 12981, 2]-NRT-code) (see above)
- linear OOA(95, 6491, F9, 2, 2) (dual of [(6491, 2), 12977, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(95, 7381, F9, 2, 2) (dual of [(7381, 2), 14757, 3]-NRT-code), using
- appending kth column [i] based on linear OA(95, 7381, F9, 2) (dual of [7381, 7376, 3]-code), using
- Hamming code H(5,9) [i]
- appending kth column [i] based on linear OA(95, 7381, F9, 2) (dual of [7381, 7376, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(95, 7381, F9, 2, 2) (dual of [(7381, 2), 14757, 3]-NRT-code), using
- linear OOA(916, 6491, F9, 2, 5) (dual of [(6491, 2), 12966, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(92, 10, F9, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;18,9) [i]
- linear OOA(914, 6481, F9, 2, 5) (dual of [(6481, 2), 12948, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), using
- trace code [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- OOA 2-folding [i] based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), using
- linear OOA(92, 10, F9, 2, 2) (dual of [(10, 2), 18, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(90, 6491, F9, 2, 0) (dual of [(6491, 2), 12982, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(924, 58419, F9, 2, 5) (dual of [(58419, 2), 116814, 6]-NRT-code), using
(19, 24, 147036)-Net over F9 — Digital
Digital (19, 24, 147036)-net over F9, using
(19, 24, large)-Net in Base 9 — Upper bound on s
There is no (19, 24, large)-net in base 9, because
- 3 times m-reduction [i] would yield (19, 21, large)-net in base 9, but