Information on Result #1746222
Digital (44, 67, 59049)-net over F81, using net defined by OOA based on linear OOA(8167, 59049, F81, 28, 23) (dual of [(59049, 28), 1653305, 24]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8167, 177148, F81, 4, 23) (dual of [(177148, 4), 708525, 24]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8167, 177148, F81, 3, 23) (dual of [(177148, 3), 531377, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8167, 531444, F81, 23) (dual of [531444, 531377, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(8167, 531441, F81, 23) (dual of [531441, 531374, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8164, 531441, F81, 22) (dual of [531441, 531377, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 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(22) ⊂ Ce(21) [i] based on
- OOA 3-folding [i] based on linear OA(8167, 531444, F81, 23) (dual of [531444, 531377, 24]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8167, 177148, F81, 3, 23) (dual of [(177148, 3), 531377, 24]-NRT-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
None.