Best Known (166, 166+17, s)-Nets in Base 3
(166, 166+17, 1048597)-Net over F3 — Constructive and digital
Digital (166, 183, 1048597)-net over F3, using
- 33 times duplication [i] based on digital (163, 180, 1048597)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (6, 14, 22)-net over F3, using
- digital (149, 166, 1048575)-net over F3, using
- net defined by OOA [i] based on linear OOA(3166, 1048575, F3, 17, 17) (dual of [(1048575, 17), 17825609, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3166, 8388601, F3, 17) (dual of [8388601, 8388435, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3166, 8388601, F3, 17) (dual of [8388601, 8388435, 18]-code), using
- net defined by OOA [i] based on linear OOA(3166, 1048575, F3, 17, 17) (dual of [(1048575, 17), 17825609, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
(166, 166+17, 4194326)-Net over F3 — Digital
Digital (166, 183, 4194326)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3183, 4194326, F3, 2, 17) (dual of [(4194326, 2), 8388469, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(317, 25, F3, 2, 8) (dual of [(25, 2), 33, 9]-NRT-code), using
- linear OOA(3166, 4194301, F3, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- OOA 2-folding [i] based on linear OA(3166, 8388602, F3, 17) (dual of [8388602, 8388436, 18]-code), using
- (u, u+v)-construction [i] based on
(166, 166+17, large)-Net in Base 3 — Upper bound on s
There is no (166, 183, large)-net in base 3, because
- 15 times m-reduction [i] would yield (166, 168, large)-net in base 3, but