Best Known (105−8, 105, s)-Nets in Base 3
(105−8, 105, 4194300)-Net over F3 — Constructive and digital
Digital (97, 105, 4194300)-net over F3, using
- net defined by OOA [i] based on linear OOA(3105, 4194300, F3, 10, 8) (dual of [(4194300, 10), 41942895, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3105, 8388601, F3, 2, 8) (dual of [(8388601, 2), 16777097, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3105, 8388602, F3, 2, 8) (dual of [(8388602, 2), 16777099, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(329, 4782968, F3, 2, 4) (dual of [(4782968, 2), 9565907, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (25, 29, 4782968)-net over F3, using
- linear OOA(376, 4194301, F3, 2, 8) (dual of [(4194301, 2), 8388526, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(376, 8388602, F3, 8) (dual of [8388602, 8388526, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(376, large, F3, 8) (dual of [large, large−76, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(376, large, F3, 8) (dual of [large, large−76, 9]-code), using
- OOA 2-folding [i] based on linear OA(376, 8388602, F3, 8) (dual of [8388602, 8388526, 9]-code), using
- linear OOA(329, 4782968, F3, 2, 4) (dual of [(4782968, 2), 9565907, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3105, 8388602, F3, 2, 8) (dual of [(8388602, 2), 16777099, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(3105, 8388601, F3, 2, 8) (dual of [(8388601, 2), 16777097, 9]-NRT-code), using
(105−8, 105, large)-Net over F3 — Digital
Digital (97, 105, large)-net over F3, using
- 35 times duplication [i] based on digital (92, 100, large)-net over F3, using
- t-expansion [i] based on digital (91, 100, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3100, large, F3, 9) (dual of [large, large−100, 10]-code), using
- 10 times code embedding in larger space [i] based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 10 times code embedding in larger space [i] based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3100, large, F3, 9) (dual of [large, large−100, 10]-code), using
- t-expansion [i] based on digital (91, 100, large)-net over F3, using
(105−8, 105, large)-Net in Base 3 — Upper bound on s
There is no (97, 105, large)-net in base 3, because
- 6 times m-reduction [i] would yield (97, 99, large)-net in base 3, but