Best Known (89, 116, s)-Nets in Base 8
(89, 116, 2520)-Net over F8 — Constructive and digital
Digital (89, 116, 2520)-net over F8, using
- net defined by OOA [i] based on linear OOA(8116, 2520, F8, 27, 27) (dual of [(2520, 27), 67924, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8116, 32761, F8, 27) (dual of [32761, 32645, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(8116, 32761, F8, 27) (dual of [32761, 32645, 28]-code), using
(89, 116, 20722)-Net over F8 — Digital
Digital (89, 116, 20722)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8116, 20722, F8, 27) (dual of [20722, 20606, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(8116, 32768, F8, 27) (dual of [32768, 32652, 28]-code), using
(89, 116, large)-Net in Base 8 — Upper bound on s
There is no (89, 116, large)-net in base 8, because
- 25 times m-reduction [i] would yield (89, 91, large)-net in base 8, but