Best Known (148, 163, s)-Nets in Base 3
(148, 163, 1198397)-Net over F3 — Constructive and digital
Digital (148, 163, 1198397)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 13, 26)-net over F3, using
- digital (135, 150, 1198371)-net over F3, using
- net defined by OOA [i] based on linear OOA(3150, 1198371, F3, 15, 15) (dual of [(1198371, 15), 17975415, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3150, 8388598, F3, 15) (dual of [8388598, 8388448, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3150, 8388598, F3, 15) (dual of [8388598, 8388448, 16]-code), using
- net defined by OOA [i] based on linear OOA(3150, 1198371, F3, 15, 15) (dual of [(1198371, 15), 17975415, 16]-NRT-code), using
(148, 163, 4194327)-Net over F3 — Digital
Digital (148, 163, 4194327)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3163, 4194327, F3, 2, 15) (dual of [(4194327, 2), 8388491, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(313, 26, F3, 2, 7) (dual of [(26, 2), 39, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 13, 26)-net over F3, using
- linear OOA(3150, 4194301, F3, 2, 15) (dual of [(4194301, 2), 8388452, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3150, 8388602, F3, 15) (dual of [8388602, 8388452, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- OOA 2-folding [i] based on linear OA(3150, 8388602, F3, 15) (dual of [8388602, 8388452, 16]-code), using
- linear OOA(313, 26, F3, 2, 7) (dual of [(26, 2), 39, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(148, 163, large)-Net in Base 3 — Upper bound on s
There is no (148, 163, large)-net in base 3, because
- 13 times m-reduction [i] would yield (148, 150, large)-net in base 3, but