Information on Result #1812291
Digital (18, 26, 531526)-net over F81, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8126, 531526, F81, 8) (dual of [531526, 531500, 9]-code), using
- (u, u+v)-construction [i] based on
- linear OA(814, 82, F81, 4) (dual of [82, 78, 5]-code or 82-arc in PG(3,81)), using
- extended Reed–Solomon code RSe(78,81) [i]
- linear OA(8122, 531444, F81, 8) (dual of [531444, 531422, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(8122, 531441, F81, 8) (dual of [531441, 531419, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(7) ⊂ Ce(6) [i] based on
- linear OA(814, 82, F81, 4) (dual of [82, 78, 5]-code or 82-arc in PG(3,81)), 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.