Information on Result #1740832
Digital (18, 31, 457)-net over F32, using net defined by OOA based on linear OOA(3231, 457, F32, 14, 13) (dual of [(457, 14), 6367, 14]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(3231, 1372, F32, 2, 13) (dual of [(1372, 2), 2713, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3231, 1373, F32, 2, 13) (dual of [(1373, 2), 2715, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3231, 1373, F32, 13) (dual of [1373, 1342, 14]-code), using
- 340 step Varšamov–Edel lengthening with (ri) = (3, 5 times 0, 1, 25 times 0, 1, 87 times 0, 1, 219 times 0) [i] based on linear OA(3225, 1027, F32, 13) (dual of [1027, 1002, 14]-code), using
- construction XX applied to C1 = C([1022,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1022,11]) [i] based on
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3225, 1023, F32, 13) (dual of [1023, 998, 14]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([1022,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([1022,11]) [i] based on
- 340 step Varšamov–Edel lengthening with (ri) = (3, 5 times 0, 1, 25 times 0, 1, 87 times 0, 1, 219 times 0) [i] based on linear OA(3225, 1027, F32, 13) (dual of [1027, 1002, 14]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3231, 1373, F32, 13) (dual of [1373, 1342, 14]-code), using
- discarding factors / shortening the dual code based on linear OOA(3231, 1373, F32, 2, 13) (dual of [(1373, 2), 2715, 14]-NRT-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.