Information on Result #1199194
Digital (14, 27, 172)-net over F32, using net defined by OOA based on linear OOA(3227, 172, F32, 13, 13) (dual of [(172, 13), 2209, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(3227, 1033, F32, 13) (dual of [1033, 1006, 14]-code), using
- construction XX applied to C1 = C([1020,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([1020,9]) [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 = {−3,−2,…,8}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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 = {−3,−2,…,9}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(3217, 1023, F32, 9) (dual of [1023, 1006, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(322, 8, F32, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- 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
- construction XX applied to C1 = C([1020,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([1020,9]) [i] based on
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (15, 28, 172)-net over F32 | [i] | Net Duplication | |
| 2 | Digital (14, 26, 172)-net over F32 | [i] | m-Reduction | |