Best Known (54, 71, s)-Nets in Base 8
(54, 71, 4096)-Net over F8 — Constructive and digital
Digital (54, 71, 4096)-net over F8, using
- net defined by OOA [i] based on linear OOA(871, 4096, F8, 17, 17) (dual of [(4096, 17), 69561, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, 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(871, 32769, F8, 17) (dual of [32769, 32698, 18]-code), using
(54, 71, 16384)-Net over F8 — Digital
Digital (54, 71, 16384)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(871, 16384, F8, 2, 17) (dual of [(16384, 2), 32697, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(871, 32768, F8, 17) (dual of [32768, 32697, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 2-folding [i] based on linear OA(871, 32768, F8, 17) (dual of [32768, 32697, 18]-code), using
(54, 71, large)-Net in Base 8 — Upper bound on s
There is no (54, 71, large)-net in base 8, because
- 15 times m-reduction [i] would yield (54, 56, large)-net in base 8, but