Best Known (3, 8, s)-Nets in Base 256
(3, 8, 32640)-Net over F256 — Constructive and digital
Digital (3, 8, 32640)-net over F256, using
- 2561 times duplication [i] based on digital (2, 7, 32640)-net over F256, using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- net defined by OOA [i] based on linear OOA(2567, 32640, F256, 5, 5) (dual of [(32640, 5), 163193, 6]-NRT-code), using
(3, 8, 32641)-Net over F256 — Digital
Digital (3, 8, 32641)-net over F256, using
- net defined by OOA [i] based on linear OOA(2568, 32641, F256, 5, 5) (dual of [(32641, 5), 163197, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(2568, 32641, F256, 4, 5) (dual of [(32641, 4), 130556, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2568, 32641, F256, 2, 5) (dual of [(32641, 2), 65274, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2568, 65282, F256, 5) (dual of [65282, 65274, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OOA 2-folding [i] based on linear OA(2568, 65282, F256, 5) (dual of [65282, 65274, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2568, 32641, F256, 2, 5) (dual of [(32641, 2), 65274, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(2568, 32641, F256, 4, 5) (dual of [(32641, 4), 130556, 6]-NRT-code), using
(3, 8, 1488725)-Net in Base 256 — Upper bound on s
There is no (3, 8, 1488726)-net in base 256, because
- 1 times m-reduction [i] would yield (3, 7, 1488726)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 72057 668825 212786 > 2567 [i]