Best Known (85−17, 85, s)-Nets in Base 8
(85−17, 85, 32768)-Net over F8 — Constructive and digital
Digital (68, 85, 32768)-net over F8, using
- net defined by OOA [i] based on linear OOA(885, 32768, F8, 17, 17) (dual of [(32768, 17), 556971, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using
(85−17, 85, 131072)-Net over F8 — Digital
Digital (68, 85, 131072)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(885, 131072, F8, 2, 17) (dual of [(131072, 2), 262059, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 2-folding [i] based on linear OA(885, 262144, F8, 17) (dual of [262144, 262059, 18]-code), using
(85−17, 85, large)-Net in Base 8 — Upper bound on s
There is no (68, 85, large)-net in base 8, because
- 15 times m-reduction [i] would yield (68, 70, large)-net in base 8, but