Best Known (220, 220+7, s)-Nets in Base 2
(220, 220+7, large)-Net over F2 — Constructive and digital
Digital (220, 227, large)-net over F2, using
- 23 times duplication [i] based on digital (217, 224, large)-net over F2, using
- t-expansion [i] based on digital (214, 224, large)-net over F2, using
- trace code for nets [i] based on digital (46, 56, 2796200)-net over F16, using
- net defined by OOA [i] based on linear OOA(1656, 2796200, F16, 14, 10) (dual of [(2796200, 14), 39146744, 11]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(1656, 8388601, F16, 2, 10) (dual of [(8388601, 2), 16777146, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1656, 8388602, F16, 2, 10) (dual of [(8388602, 2), 16777148, 11]-NRT-code), using
- trace code [i] based on linear OOA(25628, 4194301, F256, 2, 10) (dual of [(4194301, 2), 8388574, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25628, 8388602, F256, 10) (dual of [8388602, 8388574, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(25628, large, F256, 10) (dual of [large, large−28, 11]-code), using
- OOA 2-folding [i] based on linear OA(25628, 8388602, F256, 10) (dual of [8388602, 8388574, 11]-code), using
- trace code [i] based on linear OOA(25628, 4194301, F256, 2, 10) (dual of [(4194301, 2), 8388574, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1656, 8388602, F16, 2, 10) (dual of [(8388602, 2), 16777148, 11]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(1656, 8388601, F16, 2, 10) (dual of [(8388601, 2), 16777146, 11]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1656, 2796200, F16, 14, 10) (dual of [(2796200, 14), 39146744, 11]-NRT-code), using
- trace code for nets [i] based on digital (46, 56, 2796200)-net over F16, using
- t-expansion [i] based on digital (214, 224, large)-net over F2, using
(220, 220+7, large)-Net in Base 2 — Upper bound on s
There is no (220, 227, large)-net in base 2, because
- 5 times m-reduction [i] would yield (220, 222, large)-net in base 2, but