Best Known (168−7, 168, s)-Nets in Base 4
(168−7, 168, large)-Net over F4 — Constructive and digital
Digital (161, 168, large)-net over F4, using
- 3 times m-reduction [i] based on digital (161, 171, large)-net over F4, using
- trace code for nets [i] based on digital (47, 57, 2796233)-net over F64, using
- net defined by OOA [i] based on linear OOA(6457, 2796233, F64, 15, 10) (dual of [(2796233, 15), 41943438, 11]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6457, 5592467, F64, 3, 10) (dual of [(5592467, 3), 16777344, 11]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(643, 65, F64, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;192,64) [i]
- linear OOA(6417, 2796201, F64, 3, 5) (dual of [(2796201, 3), 8388586, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6417, 4194301, F64, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(6417, large, F64, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(6417, large, F64, 5) (dual of [large, large−17, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(6417, 4194301, F64, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
- linear OOA(6437, 2796201, F64, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 3-folding [i] based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- linear OOA(643, 65, F64, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6457, 5592467, F64, 3, 10) (dual of [(5592467, 3), 16777344, 11]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6457, 2796233, F64, 15, 10) (dual of [(2796233, 15), 41943438, 11]-NRT-code), using
- trace code for nets [i] based on digital (47, 57, 2796233)-net over F64, using
(168−7, 168, large)-Net in Base 4 — Upper bound on s
There is no (161, 168, large)-net in base 4, because
- 5 times m-reduction [i] would yield (161, 163, large)-net in base 4, but