Information on Result #1179516
Digital (6, 10, 258)-net over F8, using net defined by OOA based on linear OOA(810, 258, F8, 4, 4) (dual of [(258, 4), 1022, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(810, 258, F8, 3, 4) (dual of [(258, 3), 764, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(810, 516, F8, 4) (dual of [516, 506, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(810, 517, F8, 4) (dual of [517, 507, 5]-code), using
- construction XX applied to C1 = C([510,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([510,2]) [i] based on
- linear OA(87, 511, F8, 3) (dual of [511, 504, 4]-code or 511-cap in PG(6,8)), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(87, 511, F8, 3) (dual of [511, 504, 4]-code or 511-cap in PG(6,8)), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(810, 511, F8, 4) (dual of [511, 501, 5]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(84, 511, F8, 2) (dual of [511, 507, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C([510,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([510,2]) [i] based on
- discarding factors / shortening the dual code based on linear OA(810, 517, F8, 4) (dual of [517, 507, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(810, 516, F8, 4) (dual of [516, 506, 5]-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 (60, 68, 4194558)-net over F8 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (67, 76, 4194558)-net over F8 | [i] | ||
| 3 | Digital (156, 170, 4793760)-net over F8 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 4 | Digital (158, 172, 4793959)-net over F8 | [i] | ||
| 5 | Digital (154, 168, 4793751)-net over F8 | [i] | ||
| 6 | Digital (155, 169, 4793807)-net over F8 | [i] | ||
| 7 | Digital (156, 170, 4793950)-net over F8 | [i] | ||
| 8 | Digital (151, 165, 4793742)-net over F8 | [i] | ||
| 9 | Digital (136, 149, 5592658)-net over F8 | [i] | ||
| 10 | Digital (129, 141, 5592658)-net over F8 | [i] | ||