Best Known (96, 112, s)-Nets in Base 8
(96, 112, 1048575)-Net over F8 — Constructive and digital
Digital (96, 112, 1048575)-net over F8, using
- net defined by OOA [i] based on linear OOA(8112, 1048575, F8, 16, 16) (dual of [(1048575, 16), 16777088, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(8112, 8388600, F8, 16) (dual of [8388600, 8388488, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(8112, 8388600, F8, 16) (dual of [8388600, 8388488, 17]-code), using
(96, 112, large)-Net over F8 — Digital
Digital (96, 112, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8112, large, F8, 16) (dual of [large, large−112, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
(96, 112, large)-Net in Base 8 — Upper bound on s
There is no (96, 112, large)-net in base 8, because
- 14 times m-reduction [i] would yield (96, 98, large)-net in base 8, but