Best Known (219−6, 219, s)-Nets in Base 2
(219−6, 219, large)-Net over F2 — Constructive and digital
Digital (213, 219, large)-net over F2, using
- t-expansion [i] based on digital (212, 219, large)-net over F2, using
- 3 times m-reduction [i] based on digital (212, 222, large)-net over F2, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F64, using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(6437, large, F64, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(6437, 8388600, F64, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(6437, 1677720, F64, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F64, using
- 3 times m-reduction [i] based on digital (212, 222, large)-net over F2, using
(219−6, 219, large)-Net in Base 2 — Upper bound on s
There is no (213, 219, large)-net in base 2, because
- 4 times m-reduction [i] would yield (213, 215, large)-net in base 2, but