Information on Result #1207981
Digital (123, 134, 1913197)-net over F3, using (u, u+v)-construction based on
- digital (1, 6, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (117, 128, 1913190)-net over F3, using
- trace code for nets [i] based on digital (53, 64, 956595)-net over F9, using
- net defined by OOA [i] based on linear OOA(964, 956595, F9, 11, 11) (dual of [(956595, 11), 10522481, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(964, 4782976, F9, 11) (dual of [4782976, 4782912, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(964, 4782969, F9, 11) (dual of [4782969, 4782905, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(90, 7, F9, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(964, 4782976, F9, 11) (dual of [4782976, 4782912, 12]-code), using
- net defined by OOA [i] based on linear OOA(964, 956595, F9, 11, 11) (dual of [(956595, 11), 10522481, 12]-NRT-code), using
- trace code for nets [i] based on digital (53, 64, 956595)-net over F9, 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3134, 1913197, F3, 5, 11) (dual of [(1913197, 5), 9565851, 12]-NRT-code) | [i] | Extracting Embedded OOA | |