Best Known (156, 156+17, s)-Nets in Base 3
(156, 156+17, 1048575)-Net over F3 — Constructive and digital
Digital (156, 173, 1048575)-net over F3, using
- 37 times duplication [i] based on 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
(156, 156+17, 2796203)-Net over F3 — Digital
Digital (156, 173, 2796203)-net over F3, using
- 31 times duplication [i] based on digital (155, 172, 2796203)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3172, 2796203, F3, 3, 17) (dual of [(2796203, 3), 8388437, 18]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3166, 2796201, F3, 3, 17) (dual of [(2796201, 3), 8388437, 18]-NRT-code), using
- OOA 3-folding [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]
- OOA 3-folding [i] based on linear OA(3166, large, F3, 17) (dual of [large, large−166, 18]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3166, 2796201, F3, 3, 17) (dual of [(2796201, 3), 8388437, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3172, 2796203, F3, 3, 17) (dual of [(2796203, 3), 8388437, 18]-NRT-code), using
(156, 156+17, large)-Net in Base 3 — Upper bound on s
There is no (156, 173, large)-net in base 3, because
- 15 times m-reduction [i] would yield (156, 158, large)-net in base 3, but