Information on Result #1227560
Digital (35, 44, 2362874)-net over F81, using (u, u+v)-construction based on
- digital (7, 11, 265724)-net over F81, using
- net defined by OOA [i] based on linear OOA(8111, 265724, F81, 4, 4) (dual of [(265724, 4), 1062885, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(8111, 531448, F81, 4) (dual of [531448, 531437, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(814, 531441, F81, 2) (dual of [531441, 531437, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(8111, 531448, F81, 4) (dual of [531448, 531437, 5]-code), using
- net defined by OOA [i] based on linear OOA(8111, 265724, F81, 4, 4) (dual of [(265724, 4), 1062885, 5]-NRT-code), using
- digital (24, 33, 2097150)-net over F81, using
- net defined by OOA [i] based on linear OOA(8133, 2097150, F81, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(8133, 8388601, F81, 9) (dual of [8388601, 8388568, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8133, large, F81, 9) (dual of [large, large−33, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(8133, 8388601, F81, 9) (dual of [8388601, 8388568, 10]-code), using
- net defined by OOA [i] based on linear OOA(8133, 2097150, F81, 9, 9) (dual of [(2097150, 9), 18874317, 10]-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.