Information on Result #1210432
Digital (229, 244, 6425879)-net over F4, using (u, u+v)-construction based on
- digital (66, 73, 2830766)-net over F4, using
- net defined by OOA [i] based on linear OOA(473, 2830766, F4, 9, 7) (dual of [(2830766, 9), 25476821, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(473, 2830767, F4, 3, 7) (dual of [(2830767, 3), 8492228, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(412, 34566, F4, 3, 3) (dual of [(34566, 3), 103686, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(412, 34566, F4, 2, 3) (dual of [(34566, 2), 69120, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(412, 34566, F4, 3) (dual of [34566, 34554, 4]-code or 34566-cap in PG(11,4)), using
- appending kth column [i] based on linear OOA(412, 34566, F4, 2, 3) (dual of [(34566, 2), 69120, 4]-NRT-code), using
- linear OOA(461, 2796201, F4, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(461, large, F4, 7) (dual of [large, large−61, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OOA 3-folding [i] based on linear OA(461, large, F4, 7) (dual of [large, large−61, 8]-code), using
- linear OOA(412, 34566, F4, 3, 3) (dual of [(34566, 3), 103686, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(473, 2830767, F4, 3, 7) (dual of [(2830767, 3), 8492228, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(473, 2830766, F4, 9, 7) (dual of [(2830766, 9), 25476821, 8]-NRT-code), using
- digital (156, 171, 3595113)-net over F4, using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F64, using
- net defined by OOA [i] based on linear OOA(6457, 1198371, F64, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6457, 8388598, F64, 15) (dual of [8388598, 8388541, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6457, large, F64, 15) (dual of [large, large−57, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(6457, 8388598, F64, 15) (dual of [8388598, 8388541, 16]-code), using
- net defined by OOA [i] based on linear OOA(6457, 1198371, F64, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F64, 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.