Best Known (221, 221+7, s)-Nets in Base 2
(221, 221+7, large)-Net over F2 — Constructive and digital
Digital (221, 228, large)-net over F2, using
- 3 times m-reduction [i] based on digital (221, 231, large)-net over F2, using
- trace code for nets [i] based on digital (67, 77, 2796201)-net over F8, using
- net defined by OOA [i] based on linear OOA(877, 2796201, F8, 15, 10) (dual of [(2796201, 15), 41942938, 11]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(877, 5592403, F8, 3, 10) (dual of [(5592403, 3), 16777132, 11]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(874, 5592402, F8, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
- trace code [i] based on 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
- trace code [i] based on linear OOA(6437, 2796201, F64, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(874, 5592402, F8, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(877, 5592403, F8, 3, 10) (dual of [(5592403, 3), 16777132, 11]-NRT-code), using
- net defined by OOA [i] based on linear OOA(877, 2796201, F8, 15, 10) (dual of [(2796201, 15), 41942938, 11]-NRT-code), using
- trace code for nets [i] based on digital (67, 77, 2796201)-net over F8, using
(221, 221+7, large)-Net in Base 2 — Upper bound on s
There is no (221, 228, large)-net in base 2, because
- 5 times m-reduction [i] would yield (221, 223, large)-net in base 2, but