Best Known (172−25, 172, s)-Nets in Base 8
(172−25, 172, 699050)-Net over F8 — Constructive and digital
Digital (147, 172, 699050)-net over F8, using
- 83 times duplication [i] based on digital (144, 169, 699050)-net over F8, using
- net defined by OOA [i] based on linear OOA(8169, 699050, F8, 25, 25) (dual of [(699050, 25), 17476081, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8169, 8388601, F8, 25) (dual of [8388601, 8388432, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8169, large, F8, 25) (dual of [large, large−169, 26]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(8169, large, F8, 25) (dual of [large, large−169, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8169, 8388601, F8, 25) (dual of [8388601, 8388432, 26]-code), using
- net defined by OOA [i] based on linear OOA(8169, 699050, F8, 25, 25) (dual of [(699050, 25), 17476081, 26]-NRT-code), using
(172−25, 172, 6976460)-Net over F8 — Digital
Digital (147, 172, 6976460)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8172, 6976460, F8, 25) (dual of [6976460, 6976288, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8172, large, F8, 25) (dual of [large, large−172, 26]-code), using
- 3 times code embedding in larger space [i] based on linear OA(8169, large, F8, 25) (dual of [large, large−169, 26]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 3 times code embedding in larger space [i] based on linear OA(8169, large, F8, 25) (dual of [large, large−169, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(8172, large, F8, 25) (dual of [large, large−172, 26]-code), using
(172−25, 172, large)-Net in Base 8 — Upper bound on s
There is no (147, 172, large)-net in base 8, because
- 23 times m-reduction [i] would yield (147, 149, large)-net in base 8, but