Information on Result #1812224
Digital (9, 16, 6645)-net over F81, using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8116, 6645, F81, 7) (dual of [6645, 6629, 8]-code), using
- (u, u+v)-construction [i] based on
- linear OA(813, 82, F81, 3) (dual of [82, 79, 4]-code or 82-arc in PG(2,81) or 82-cap in PG(2,81)), using
- extended Reed–Solomon code RSe(79,81) [i]
- oval in PG(2, 81) [i]
- linear OA(8113, 6563, F81, 7) (dual of [6563, 6550, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8113, 6561, F81, 7) (dual of [6561, 6548, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 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(6) ⊂ Ce(5) [i] based on
- linear OA(813, 82, F81, 3) (dual of [82, 79, 4]-code or 82-arc in PG(2,81) or 82-cap in PG(2,81)), 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.