Best Known (239, 239+8, s)-Nets in Base 2
(239, 239+8, large)-Net over F2 — Constructive and digital
Digital (239, 247, large)-net over F2, using
- t-expansion [i] based on digital (237, 247, large)-net over F2, using
- 1 times m-reduction [i] based on digital (237, 248, large)-net over F2, using
- trace code for nets [i] based on digital (51, 62, 2796200)-net over F16, using
- net defined by OOA [i] based on linear OOA(1662, 2796200, F16, 14, 11) (dual of [(2796200, 14), 39146738, 12]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(1662, 8388601, F16, 2, 11) (dual of [(8388601, 2), 16777140, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1662, 8388602, F16, 2, 11) (dual of [(8388602, 2), 16777142, 12]-NRT-code), using
- trace code [i] based on linear OOA(25631, 4194301, F256, 2, 11) (dual of [(4194301, 2), 8388571, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25631, 8388602, F256, 11) (dual of [8388602, 8388571, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- OOA 2-folding [i] based on linear OA(25631, 8388602, F256, 11) (dual of [8388602, 8388571, 12]-code), using
- trace code [i] based on linear OOA(25631, 4194301, F256, 2, 11) (dual of [(4194301, 2), 8388571, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1662, 8388602, F16, 2, 11) (dual of [(8388602, 2), 16777142, 12]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(1662, 8388601, F16, 2, 11) (dual of [(8388601, 2), 16777140, 12]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1662, 2796200, F16, 14, 11) (dual of [(2796200, 14), 39146738, 12]-NRT-code), using
- trace code for nets [i] based on digital (51, 62, 2796200)-net over F16, using
- 1 times m-reduction [i] based on digital (237, 248, large)-net over F2, using
(239, 239+8, large)-Net in Base 2 — Upper bound on s
There is no (239, 247, large)-net in base 2, because
- 6 times m-reduction [i] would yield (239, 241, large)-net in base 2, but