Information on Result #1749914
Digital (74, 93, 348)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(293, 348, F2, 3, 19) (dual of [(348, 3), 951, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(293, 1044, F2, 19) (dual of [1044, 951, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(293, 1045, F2, 19) (dual of [1045, 952, 20]-code), using
- construction XX applied to C1 = C([1021,14]), C2 = C([0,16]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([1021,16]) [i] based on
- linear OA(281, 1023, F2, 17) (dual of [1023, 942, 18]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(281, 1023, F2, 17) (dual of [1023, 942, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(271, 1023, F2, 15) (dual of [1023, 952, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code) (see above)
- construction XX applied to C1 = C([1021,14]), C2 = C([0,16]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([1021,16]) [i] based on
- discarding factors / shortening the dual code based on linear OA(293, 1045, F2, 19) (dual of [1045, 952, 20]-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.