Information on Result #1198772
Digital (9, 15, 684)-net over F32, using net defined by OOA based on linear OOA(3215, 684, F32, 6, 6) (dual of [(684, 6), 4089, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(3215, 2052, F32, 6) (dual of [2052, 2037, 7]-code), using
- (u, u+v)-construction [i] based on
- linear OA(324, 1025, F32, 3) (dual of [1025, 1021, 4]-code or 1025-cap in PG(3,32)), using
- linear OA(3211, 1027, F32, 6) (dual of [1027, 1016, 7]-code), using
- construction XX applied to C1 = C([1022,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([1022,4]) [i] based on
- linear OA(329, 1023, F32, 5) (dual of [1023, 1014, 6]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(329, 1023, F32, 5) (dual of [1023, 1014, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3211, 1023, F32, 6) (dual of [1023, 1012, 7]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(327, 1023, F32, 4) (dual of [1023, 1016, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [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([1022,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([1022,4]) [i] based on
- (u, u+v)-construction [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 (59, 71, 1398784)-net over F32 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (63, 76, 1398784)-net over F32 | [i] | ||