Information on Result #1209898
Digital (34, 40, 87389)-net over F4, using (u, u+v)-construction based on
- digital (0, 3, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (31, 37, 87384)-net over F4, using
- net defined by OOA [i] based on linear OOA(437, 87384, F4, 6, 6) (dual of [(87384, 6), 524267, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(437, 262152, F4, 6) (dual of [262152, 262115, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(437, 262153, F4, 6) (dual of [262153, 262116, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(437, 262144, F4, 6) (dual of [262144, 262107, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(428, 262144, F4, 5) (dual of [262144, 262116, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(437, 262153, F4, 6) (dual of [262153, 262116, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(437, 262152, F4, 6) (dual of [262152, 262115, 7]-code), using
- net defined by OOA [i] based on linear OOA(437, 87384, F4, 6, 6) (dual of [(87384, 6), 524267, 7]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (164, 176, 5679789)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (175, 188, 5679789)-net over F4 | [i] | ||