Information on Result #1811354
Digital (36, 55, 103786)-net over F64, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(6455, 103786, F64, 2, 19) (dual of [(103786, 2), 207517, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6455, 131073, F64, 2, 19) (dual of [(131073, 2), 262091, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6455, 262146, F64, 19) (dual of [262146, 262091, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(6455, 262147, F64, 19) (dual of [262147, 262092, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(6455, 262144, F64, 19) (dual of [262144, 262089, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(6455, 262147, F64, 19) (dual of [262147, 262092, 20]-code), using
- OOA 2-folding [i] based on linear OA(6455, 262146, F64, 19) (dual of [262146, 262091, 20]-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 | (47, 66, 103786)-net in base 32 | [i] | Base Change | |