Information on Result #1789758
Digital (29, 46, 359)-net over F7, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(746, 359, F7, 17) (dual of [359, 313, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(746, 360, F7, 17) (dual of [360, 314, 18]-code), using
- 9 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 6 times 0) [i] based on linear OA(743, 348, F7, 17) (dual of [348, 305, 18]-code), using
- construction XX applied to C1 = C([341,14]), C2 = C([0,15]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([341,15]) [i] based on
- linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,14}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(743, 342, F7, 17) (dual of [342, 299, 18]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(737, 342, F7, 15) (dual of [342, 305, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(70, 3, F7, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C([341,14]), C2 = C([0,15]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([341,15]) [i] based on
- 9 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 6 times 0) [i] based on linear OA(743, 348, F7, 17) (dual of [348, 305, 18]-code), using
Mode: 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.