Best Known (61, 61+6, s)-Nets in Base 3
(61, 61+6, 2796313)-Net over F3 — Constructive and digital
Digital (61, 67, 2796313)-net over F3, using
- net defined by OOA [i] based on linear OOA(367, 2796313, F3, 6, 6) (dual of [(2796313, 6), 16777811, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(367, 2796313, F3, 5, 6) (dual of [(2796313, 5), 13981498, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(37, 112, F3, 5, 3) (dual of [(112, 5), 553, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(37, 112, F3, 3, 3) (dual of [(112, 3), 329, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(37, 112, F3, 2, 3) (dual of [(112, 2), 217, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(37, 112, F3, 3, 3) (dual of [(112, 3), 329, 4]-NRT-code), using
- linear OOA(360, 2796201, F3, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- linear OOA(37, 112, F3, 5, 3) (dual of [(112, 5), 553, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(367, 2796313, F3, 5, 6) (dual of [(2796313, 5), 13981498, 7]-NRT-code), using
(61, 61+6, large)-Net over F3 — Digital
Digital (61, 67, large)-net over F3, using
- 37 times duplication [i] based on digital (54, 60, large)-net over F3, using
- net defined by OOA [i] based on linear OOA(360, large, F3, 6, 6), using
- appending kth column [i] based on linear OOA(360, large, F3, 5, 6), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- appending kth column [i] based on linear OOA(360, large, F3, 5, 6), using
- net defined by OOA [i] based on linear OOA(360, large, F3, 6, 6), using
(61, 61+6, large)-Net in Base 3 — Upper bound on s
There is no (61, 67, large)-net in base 3, because
- 4 times m-reduction [i] would yield (61, 63, large)-net in base 3, but