Best Known (145, 145+24, s)-Nets in Base 8
(145, 145+24, 699050)-Net over F8 — Constructive and digital
Digital (145, 169, 699050)-net over F8, using
- t-expansion [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
(145, 145+24, large)-Net over F8 — Digital
Digital (145, 169, large)-net over F8, using
- 81 times duplication [i] based on digital (144, 168, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
(145, 145+24, large)-Net in Base 8 — Upper bound on s
There is no (145, 169, large)-net in base 8, because
- 22 times m-reduction [i] would yield (145, 147, large)-net in base 8, but