Best Known (94−10, 94, s)-Nets in Base 9
(94−10, 94, 3374882)-Net over F9 — Constructive and digital
Digital (84, 94, 3374882)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (15, 20, 19442)-net over F9, using
- net defined by OOA [i] based on linear OOA(920, 19442, F9, 6, 5) (dual of [(19442, 6), 116632, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(920, 19443, F9, 2, 5) (dual of [(19443, 2), 38866, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(91, 6481, F9, 2, 1) (dual of [(6481, 2), 12961, 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(95, 6481, F9, 2, 2) (dual of [(6481, 2), 12957, 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(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(91, 6481, F9, 2, 1) (dual of [(6481, 2), 12961, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(920, 19443, F9, 2, 5) (dual of [(19443, 2), 38866, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(920, 19442, F9, 6, 5) (dual of [(19442, 6), 116632, 6]-NRT-code), using
- digital (64, 74, 3355440)-net over F9, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- digital (15, 20, 19442)-net over F9, using
(94−10, 94, large)-Net over F9 — Digital
Digital (84, 94, large)-net over F9, using
- t-expansion [i] based on digital (83, 94, large)-net over F9, using
- 3 times m-reduction [i] based on digital (83, 97, large)-net over F9, using
(94−10, 94, large)-Net in Base 9 — Upper bound on s
There is no (84, 94, large)-net in base 9, because
- 8 times m-reduction [i] would yield (84, 86, large)-net in base 9, but