Information on Result #1202764
Digital (50, 69, 59109)-net over F81, using net defined by OOA based on linear OOA(8169, 59109, F81, 21, 19) (dual of [(59109, 21), 1241220, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8169, 177328, F81, 3, 19) (dual of [(177328, 3), 531915, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8169, 177330, F81, 3, 19) (dual of [(177330, 3), 531921, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8114, 182, F81, 3, 9) (dual of [(182, 3), 532, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(814, 82, F81, 3, 4) (dual of [(82, 3), 242, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;242,81) [i]
- linear OOA(8110, 100, F81, 3, 9) (dual of [(100, 3), 290, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,290P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- linear OOA(814, 82, F81, 3, 4) (dual of [(82, 3), 242, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8155, 177148, F81, 3, 19) (dual of [(177148, 3), 531389, 20]-NRT-code), using
- OOA 3-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 3-folding [i] based on linear OA(8155, 531444, F81, 19) (dual of [531444, 531389, 20]-code), using
- linear OOA(8114, 182, F81, 3, 9) (dual of [(182, 3), 532, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8169, 177330, F81, 3, 19) (dual of [(177330, 3), 531921, 20]-NRT-code), using
Mode: Constructive and 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.