Best Known (137, 152, s)-Nets in Base 3
(137, 152, 1198371)-Net over F3 — Constructive and digital
Digital (137, 152, 1198371)-net over F3, using
- 32 times duplication [i] based on digital (135, 150, 1198371)-net over F3, using
- net defined by OOA [i] based on linear OOA(3150, 1198371, F3, 15, 15) (dual of [(1198371, 15), 17975415, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3150, 8388598, F3, 15) (dual of [8388598, 8388448, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3150, 8388598, F3, 15) (dual of [8388598, 8388448, 16]-code), using
- net defined by OOA [i] based on linear OOA(3150, 1198371, F3, 15, 15) (dual of [(1198371, 15), 17975415, 16]-NRT-code), using
(137, 152, 2796201)-Net over F3 — Digital
Digital (137, 152, 2796201)-net over F3, using
- 32 times duplication [i] based on digital (135, 150, 2796201)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3150, 2796201, F3, 3, 15) (dual of [(2796201, 3), 8388453, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- OOA 3-folding [i] based on linear OA(3150, large, F3, 15) (dual of [large, large−150, 16]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3150, 2796201, F3, 3, 15) (dual of [(2796201, 3), 8388453, 16]-NRT-code), using
(137, 152, large)-Net in Base 3 — Upper bound on s
There is no (137, 152, large)-net in base 3, because
- 13 times m-reduction [i] would yield (137, 139, large)-net in base 3, but