Information on Result #1765866
Digital (152, 173, 177157)-net over F3, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3173, 177157, F3, 3, 21) (dual of [(177157, 3), 531298, 22]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3170, 177156, F3, 3, 21) (dual of [(177156, 3), 531298, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3170, 531468, F3, 21) (dual of [531468, 531298, 22]-code), using
- construction X4 applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(3169, 531442, F3, 21) (dual of [531442, 531273, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3145, 531442, F3, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 324−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(325, 26, F3, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,3)), using
- dual of repetition code with length 26 [i]
- linear OA(31, 26, F3, 1) (dual of [26, 25, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to C([0,10]) ⊂ C([0,9]) [i] based on
- OOA 3-folding [i] based on linear OA(3170, 531468, F3, 21) (dual of [531468, 531298, 22]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (153, 174, 177157)-net over F3 | [i] | Net Duplication | |