Information on Result #1813163
Digital (40, 78, 2406)-net over F81, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(8178, 2406, F81, 2, 38) (dual of [(2406, 2), 4734, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8178, 3286, F81, 2, 38) (dual of [(3286, 2), 6494, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8178, 6572, F81, 38) (dual of [6572, 6494, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- linear OA(8175, 6561, F81, 38) (dual of [6561, 6486, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(8167, 6561, F81, 34) (dual of [6561, 6494, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(813, 11, F81, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,81) or 11-cap in PG(2,81)), using
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- Reed–Solomon code RS(78,81) [i]
- discarding factors / shortening the dual code based on linear OA(813, 81, F81, 3) (dual of [81, 78, 4]-code or 81-arc in PG(2,81) or 81-cap in PG(2,81)), using
- construction X applied to Ce(37) ⊂ Ce(33) [i] based on
- OOA 2-folding [i] based on linear OA(8178, 6572, F81, 38) (dual of [6572, 6494, 39]-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.