Information on Result #1222001
Digital (88, 98, 6713900)-net over F27, using (u, u+v)-construction based on
- digital (16, 21, 4194301)-net over F27, using
- net defined by OOA [i] based on linear OOA(2721, 4194301, F27, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- net defined by OOA [i] based on linear OOA(2721, 4194301, F27, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- digital (67, 77, 3356950)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (16, 21, 4194301)-net over F27 (see above)
- digital (46, 56, 1678475)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (5, 10, 755)-net over F27, using
- net defined by OOA [i] based on linear OOA(2710, 755, F27, 6, 5) (dual of [(755, 6), 4520, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2710, 756, F27, 2, 5) (dual of [(756, 2), 1502, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(270, s, F27, 2, 0) for arbitrarily large s, using
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
- linear OOA(271, 28, F27, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(271, s, F27, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(271, s, F27, 2, 1) for arbitrarily large s, using
- linear OOA(271, 28, F27, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
- linear OOA(271, 28, F27, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
- linear OOA(272, 28, F27, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;54,27) [i]
- linear OOA(275, 28, F27, 2, 5) (dual of [(28, 2), 51, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;51,27) [i]
- linear OOA(270, 28, F27, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(2710, 756, F27, 2, 5) (dual of [(756, 2), 1502, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2710, 755, F27, 6, 5) (dual of [(755, 6), 4520, 6]-NRT-code), using
- digital (36, 46, 1677720)-net over F27, using
- net defined by OOA [i] based on linear OOA(2746, 1677720, F27, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2746, 8388600, F27, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2746, large, F27, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2746, large, F27, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2746, 8388600, F27, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2746, 1677720, F27, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- digital (5, 10, 755)-net over F27, using
- (u, u+v)-construction [i] based on
- (u, u+v)-construction [i] based on
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.