Best Known (103, 103+10, s)-Nets in Base 9
(103, 103+10, 6711720)-Net over F9 — Constructive and digital
Digital (103, 113, 6711720)-net over F9, using
- generalized (u, u+v)-construction [i] based on
- digital (3, 6, 840)-net over F9, using
- net defined by OOA [i] based on linear OOA(96, 840, F9, 3, 3) (dual of [(840, 3), 2514, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(96, 840, F9, 2, 3) (dual of [(840, 2), 1674, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(96, 840, F9, 3, 3) (dual of [(840, 3), 2514, 4]-NRT-code), using
- digital (28, 33, 3355440)-net over F9, using
- s-reduction based on digital (28, 33, 4194301)-net over F9, using
- net defined by OOA [i] based on linear OOA(933, 4194301, F9, 5, 5) (dual of [(4194301, 5), 20971472, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(933, large, F9, 5) (dual of [large, large−33, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 916−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(933, large, F9, 5) (dual of [large, large−33, 6]-code), using
- net defined by OOA [i] based on linear OOA(933, 4194301, F9, 5, 5) (dual of [(4194301, 5), 20971472, 6]-NRT-code), using
- s-reduction based on digital (28, 33, 4194301)-net over F9, using
- digital (64, 74, 3355440)-net over F9, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- digital (3, 6, 840)-net over F9, using
(103, 103+10, large)-Net over F9 — Digital
Digital (103, 113, large)-net over F9, using
- t-expansion [i] based on digital (101, 113, large)-net over F9, using
- 5 times m-reduction [i] based on digital (101, 118, large)-net over F9, using
(103, 103+10, large)-Net in Base 9 — Upper bound on s
There is no (103, 113, large)-net in base 9, because
- 8 times m-reduction [i] would yield (103, 105, large)-net in base 9, but