Best Known (132−12, 132, s)-Nets in Base 8
(132−12, 132, 5592400)-Net over F8 — Constructive and digital
Digital (120, 132, 5592400)-net over F8, using
- trace code for nets [i] based on digital (54, 66, 2796200)-net over F64, using
- net defined by OOA [i] based on linear OOA(6466, 2796200, F64, 14, 12) (dual of [(2796200, 14), 39146734, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(6466, 8388601, F64, 2, 12) (dual of [(8388601, 2), 16777136, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6466, 8388602, F64, 2, 12) (dual of [(8388602, 2), 16777138, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(6421, 4194301, F64, 2, 6) (dual of [(4194301, 2), 8388581, 7]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6421, 8388602, F64, 6) (dual of [8388602, 8388581, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(6421, large, F64, 6) (dual of [large, large−21, 7]-code), using
- OOA 2-folding [i] based on linear OA(6421, 8388602, F64, 6) (dual of [8388602, 8388581, 7]-code), using
- linear OOA(6445, 4194301, F64, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6445, 8388602, F64, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(6445, 8388602, F64, 12) (dual of [8388602, 8388557, 13]-code), using
- linear OOA(6421, 4194301, F64, 2, 6) (dual of [(4194301, 2), 8388581, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(6466, 8388602, F64, 2, 12) (dual of [(8388602, 2), 16777138, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(6466, 8388601, F64, 2, 12) (dual of [(8388601, 2), 16777136, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(6466, 2796200, F64, 14, 12) (dual of [(2796200, 14), 39146734, 13]-NRT-code), using
(132−12, 132, large)-Net over F8 — Digital
Digital (120, 132, large)-net over F8, using
- t-expansion [i] based on digital (119, 132, large)-net over F8, using
- 7 times m-reduction [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
- 7 times m-reduction [i] based on digital (119, 139, large)-net over F8, using
(132−12, 132, large)-Net in Base 8 — Upper bound on s
There is no (120, 132, large)-net in base 8, because
- 10 times m-reduction [i] would yield (120, 122, large)-net in base 8, but