Information on Result #1745918
Digital (36, 55, 59451)-net over F81, using net defined by OOA based on linear OOA(8155, 59451, F81, 21, 19) (dual of [(59451, 21), 1248416, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8155, 178354, F81, 3, 19) (dual of [(178354, 3), 535007, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8155, 178356, F81, 3, 19) (dual of [(178356, 3), 535013, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8155, 178356, F81, 2, 19) (dual of [(178356, 2), 356657, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8155, 265722, F81, 2, 19) (dual of [(265722, 2), 531389, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8155, 531444, F81, 19) (dual of [531444, 531389, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(8155, 531441, F81, 19) (dual of [531441, 531386, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(8152, 531441, F81, 18) (dual of [531441, 531389, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(8155, 531444, F81, 19) (dual of [531444, 531389, 20]-code), using
- discarding factors / shortening the dual code based on linear OOA(8155, 265722, F81, 2, 19) (dual of [(265722, 2), 531389, 20]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8155, 178356, F81, 2, 19) (dual of [(178356, 2), 356657, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8155, 178356, F81, 3, 19) (dual of [(178356, 3), 535013, 20]-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.