Information on Result #1179408
Digital (71, 77, 3188669)-net over F3, using net defined by OOA based on linear OOA(377, 3188669, F3, 6, 6) (dual of [(3188669, 6), 19131937, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(377, 3188669, F3, 5, 6) (dual of [(3188669, 5), 15943268, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(377, 3188670, F3, 3, 6) (dual of [(3188670, 3), 9565933, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(35, 20, F3, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(35, 20, F3, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
- linear OOA(372, 3188650, F3, 3, 6) (dual of [(3188650, 3), 9565878, 7]-NRT-code), using
- trace code [i] based on linear OOA(936, 1594325, F9, 3, 6) (dual of [(1594325, 3), 4782939, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(936, 4782975, F9, 6) (dual of [4782975, 4782939, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(936, 4782976, F9, 6) (dual of [4782976, 4782940, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(936, 4782969, F9, 6) (dual of [4782969, 4782933, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(929, 4782969, F9, 5) (dual of [4782969, 4782940, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(936, 4782976, F9, 6) (dual of [4782976, 4782940, 7]-code), using
- OOA 3-folding [i] based on linear OA(936, 4782975, F9, 6) (dual of [4782975, 4782939, 7]-code), using
- trace code [i] based on linear OOA(936, 1594325, F9, 3, 6) (dual of [(1594325, 3), 4782939, 7]-NRT-code), using
- linear OOA(35, 20, F3, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(377, 3188670, F3, 3, 6) (dual of [(3188670, 3), 9565933, 7]-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.