Best Known (194−18, 194, s)-Nets in Base 3
(194−18, 194, 932082)-Net over F3 — Constructive and digital
Digital (176, 194, 932082)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (5, 14, 15)-net over F3, using
- digital (162, 180, 932067)-net over F3, using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- net defined by OOA [i] based on linear OOA(3180, 932067, F3, 18, 18) (dual of [(932067, 18), 16777026, 19]-NRT-code), using
(194−18, 194, 4110430)-Net over F3 — Digital
Digital (176, 194, 4110430)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3194, 4110430, F3, 2, 18) (dual of [(4110430, 2), 8220666, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3194, 4194316, F3, 2, 18) (dual of [(4194316, 2), 8388438, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(314, 15, F3, 2, 9) (dual of [(15, 2), 16, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 14, 15)-net over F3, using
- linear OOA(3180, 4194301, F3, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- linear OOA(314, 15, F3, 2, 9) (dual of [(15, 2), 16, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(3194, 4194316, F3, 2, 18) (dual of [(4194316, 2), 8388438, 19]-NRT-code), using
(194−18, 194, large)-Net in Base 3 — Upper bound on s
There is no (176, 194, large)-net in base 3, because
- 16 times m-reduction [i] would yield (176, 178, large)-net in base 3, but