Information on Result #1840653
(51, 82, 437)-net in base 27, using net defined by OOA based on OOA(2782, 437, S27, 31, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(2782, 6556, S27, 31), using
- discarding factors based on OA(2782, 6563, S27, 31), using
- discarding parts of the base [i] based on linear OA(8161, 6563, F81, 31) (dual of [6563, 6502, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- linear OA(8161, 6561, F81, 31) (dual of [6561, 6500, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8159, 6561, F81, 30) (dual of [6561, 6502, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- discarding parts of the base [i] based on linear OA(8161, 6563, F81, 31) (dual of [6563, 6502, 32]-code), using
- discarding factors based on OA(2782, 6563, S27, 31), using
Mode: Constructive.
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 | (51, 81, 437)-net in base 27 | [i] | m-Reduction | |