Best Known (124, 124+20, s)-Nets in Base 8
(124, 124+20, 838860)-Net over F8 — Constructive and digital
Digital (124, 144, 838860)-net over F8, using
- 1 times m-reduction [i] based on digital (124, 145, 838860)-net over F8, using
- net defined by OOA [i] based on linear OOA(8145, 838860, F8, 21, 21) (dual of [(838860, 21), 17615915, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8145, 8388601, F8, 21) (dual of [8388601, 8388456, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, large, F8, 21) (dual of [large, large−145, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8145, large, F8, 21) (dual of [large, large−145, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(8145, 8388601, F8, 21) (dual of [8388601, 8388456, 22]-code), using
- net defined by OOA [i] based on linear OOA(8145, 838860, F8, 21, 21) (dual of [(838860, 21), 17615915, 22]-NRT-code), using
(124, 124+20, large)-Net over F8 — Digital
Digital (124, 144, large)-net over F8, using
- 85 times duplication [i] based on digital (119, 139, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8139, large, F8, 20) (dual of [large, large−139, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 2 times code embedding in larger space [i] based on linear OA(8137, large, F8, 20) (dual of [large, large−137, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8139, large, F8, 20) (dual of [large, large−139, 21]-code), using
(124, 124+20, large)-Net in Base 8 — Upper bound on s
There is no (124, 144, large)-net in base 8, because
- 18 times m-reduction [i] would yield (124, 126, large)-net in base 8, but