Best Known (52, 52+8, s)-Nets in Base 9
(52, 52+8, 4194301)-Net over F9 — Constructive and digital
Digital (52, 60, 4194301)-net over F9, using
- net defined by OOA [i] based on linear OOA(960, 4194301, F9, 10, 8) (dual of [(4194301, 10), 41942950, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(960, large, F9, 2, 8), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(958, 8388602, F9, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- trace code [i] based on linear OOA(8129, 4194301, F81, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8129, 8388602, F81, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(8129, 8388602, F81, 8) (dual of [8388602, 8388573, 9]-code), using
- trace code [i] based on linear OOA(8129, 4194301, F81, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(958, 8388602, F9, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(960, large, F9, 2, 8), using
(52, 52+8, large)-Net over F9 — Digital
Digital (52, 60, large)-net over F9, using
- 1 times m-reduction [i] based on digital (52, 61, large)-net over F9, using
(52, 52+8, large)-Net in Base 9 — Upper bound on s
There is no (52, 60, large)-net in base 9, because
- 6 times m-reduction [i] would yield (52, 54, large)-net in base 9, but