Information on Result #1806632
Digital (32, 68, 353)-net over F27, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2768, 353, F27, 2, 36) (dual of [(353, 2), 638, 37]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2768, 366, F27, 2, 36) (dual of [(366, 2), 664, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2768, 732, F27, 36) (dual of [732, 664, 37]-code), using
- construction XX applied to C1 = C([727,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([727,34]) [i] based on
- linear OA(2766, 728, F27, 35) (dual of [728, 662, 36]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,33}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2766, 728, F27, 35) (dual of [728, 662, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2768, 728, F27, 36) (dual of [728, 660, 37]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,34}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2764, 728, F27, 34) (dual of [728, 664, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([727,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([727,34]) [i] based on
- OOA 2-folding [i] based on linear OA(2768, 732, F27, 36) (dual of [732, 664, 37]-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.