Information on Result #1230086
Digital (133, 145, 5598963)-net over F9, using generalized (u, u+v)-construction based on
- digital (10, 14, 6563)-net over F9, using
- net defined by OOA [i] based on linear OOA(914, 6563, F9, 4, 4) (dual of [(6563, 4), 26238, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(914, 6563, F9, 3, 4) (dual of [(6563, 3), 19675, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(914, 13126, F9, 4) (dual of [13126, 13112, 5]-code), using
- trace code [i] based on linear OA(817, 6563, F81, 4) (dual of [6563, 6556, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(815, 6561, F81, 3) (dual of [6561, 6556, 4]-code or 6561-cap in PG(4,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- trace code [i] based on linear OA(817, 6563, F81, 4) (dual of [6563, 6556, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(914, 13126, F9, 4) (dual of [13126, 13112, 5]-code), using
- appending kth column [i] based on linear OOA(914, 6563, F9, 3, 4) (dual of [(6563, 3), 19675, 5]-NRT-code), using
- net defined by OOA [i] based on linear OOA(914, 6563, F9, 4, 4) (dual of [(6563, 4), 26238, 5]-NRT-code), using
- digital (35, 41, 2796200)-net over F9, using
- s-reduction based on digital (35, 41, 2796201)-net over F9, using
- net defined by OOA [i] based on linear OOA(941, 2796201, F9, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(941, large, F9, 6) (dual of [large, large−41, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(941, large, F9, 6) (dual of [large, large−41, 7]-code), using
- net defined by OOA [i] based on linear OOA(941, 2796201, F9, 6, 6) (dual of [(2796201, 6), 16777165, 7]-NRT-code), using
- s-reduction based on digital (35, 41, 2796201)-net over F9, using
- digital (78, 90, 2796200)-net over F9, using
- net defined by OOA [i] based on linear OOA(990, 2796200, F9, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(990, 8388601, F9, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(990, 8388602, F9, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- trace code [i] based on linear OOA(8145, 4194301, F81, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8145, 8388602, F81, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(8145, large, F81, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(8145, 8388602, F81, 12) (dual of [8388602, 8388557, 13]-code), using
- trace code [i] based on linear OOA(8145, 4194301, F81, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(990, 8388602, F9, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(990, 8388601, F9, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(990, 2796200, F9, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
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.