Best Known (92, 117, s)-Nets in Base 8
(92, 117, 2734)-Net over F8 — Constructive and digital
Digital (92, 117, 2734)-net over F8, using
- net defined by OOA [i] based on linear OOA(8117, 2734, F8, 25, 25) (dual of [(2734, 25), 68233, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(8117, 32809, F8, 25) (dual of [32809, 32692, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- linear OA(8106, 32768, F8, 25) (dual of [32768, 32662, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(876, 32768, F8, 18) (dual of [32768, 32692, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(811, 41, F8, 6) (dual of [41, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(811, 63, F8, 6) (dual of [63, 52, 7]-code), using
- construction X applied to Ce(24) ⊂ Ce(17) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(8117, 32809, F8, 25) (dual of [32809, 32692, 26]-code), using
(92, 117, 35398)-Net over F8 — Digital
Digital (92, 117, 35398)-net over F8, using
(92, 117, large)-Net in Base 8 — Upper bound on s
There is no (92, 117, large)-net in base 8, because
- 23 times m-reduction [i] would yield (92, 94, large)-net in base 8, but