Best Known (194, 194+17, s)-Nets in Base 3
(194, 194+17, 1051035)-Net over F3 — Constructive and digital
Digital (194, 211, 1051035)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (37, 45, 2460)-net over F3, using
- net defined by OOA [i] based on linear OOA(345, 2460, F3, 8, 8) (dual of [(2460, 8), 19635, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(345, 9840, F3, 8) (dual of [9840, 9795, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(345, 9841, F3, 8) (dual of [9841, 9796, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(345, 9840, F3, 8) (dual of [9840, 9795, 9]-code), using
- net defined by OOA [i] based on linear OOA(345, 2460, F3, 8, 8) (dual of [(2460, 8), 19635, 9]-NRT-code), 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
- digital (37, 45, 2460)-net over F3, using
(194, 194+17, large)-Net over F3 — Digital
Digital (194, 211, large)-net over F3, using
- 38 times duplication [i] based on digital (186, 203, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3203, large, F3, 17) (dual of [large, large−203, 18]-code), using
- 37 times code embedding in larger space [i] 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]
- 37 times code embedding in larger space [i] based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3203, large, F3, 17) (dual of [large, large−203, 18]-code), using
(194, 194+17, large)-Net in Base 3 — Upper bound on s
There is no (194, 211, large)-net in base 3, because
- 15 times m-reduction [i] would yield (194, 196, large)-net in base 3, but