Information on Result #1745954
Digital (20, 40, 729)-net over F81, using net defined by OOA based on linear OOA(8140, 729, F81, 28, 20) (dual of [(729, 28), 20372, 21]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8140, 2188, F81, 4, 20) (dual of [(2188, 4), 8712, 21]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8140, 2188, F81, 3, 20) (dual of [(2188, 3), 6524, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8140, 6564, F81, 20) (dual of [6564, 6524, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8140, 6566, F81, 20) (dual of [6566, 6526, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8135, 6561, F81, 18) (dual of [6561, 6526, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(8140, 6566, F81, 20) (dual of [6566, 6526, 21]-code), using
- OOA 3-folding [i] based on linear OA(8140, 6564, F81, 20) (dual of [6564, 6524, 21]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(8140, 2188, F81, 3, 20) (dual of [(2188, 3), 6524, 21]-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.