Information on Result #1811268
Digital (33, 50, 131076)-net over F64, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(6450, 131076, F64, 2, 17) (dual of [(131076, 2), 262102, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6450, 262152, F64, 17) (dual of [262152, 262102, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(6449, 262145, F64, 17) (dual of [262145, 262096, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(6443, 262145, F64, 15) (dual of [262145, 262102, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | (43, 60, 131076)-net in base 32 | [i] | Base Change | |