Information on Result #1843055
(85, 109, 44369)-net in base 27, using (u, u+v)-construction based on
- (4, 16, 82)-net in base 27, using
- base change [i] based on digital (0, 12, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- base change [i] based on digital (0, 12, 82)-net over F81, using
- digital (69, 93, 44287)-net over F27, using
- net defined by OOA [i] based on linear OOA(2793, 44287, F27, 24, 24) (dual of [(44287, 24), 1062795, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2793, 531444, F27, 24) (dual of [531444, 531351, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2793, 531445, F27, 24) (dual of [531445, 531352, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(2793, 531441, F27, 24) (dual of [531441, 531348, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2789, 531441, F27, 23) (dual of [531441, 531352, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(2793, 531445, F27, 24) (dual of [531445, 531352, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2793, 531444, F27, 24) (dual of [531444, 531351, 25]-code), using
- net defined by OOA [i] based on linear OOA(2793, 44287, F27, 24, 24) (dual of [(44287, 24), 1062795, 25]-NRT-code), using
Mode: Constructive.
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 | (86, 110, 44369)-net in base 27 | [i] | Net Duplication | |