Best Known (140, 140+15, s)-Nets in Base 3
(140, 140+15, 1198371)-Net over F3 — Constructive and digital
Digital (140, 155, 1198371)-net over F3, using
- 35 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
(140, 140+15, 3203509)-Net over F3 — Digital
Digital (140, 155, 3203509)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3155, 3203509, F3, 2, 15) (dual of [(3203509, 2), 6406863, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3155, 4194303, F3, 2, 15) (dual of [(4194303, 2), 8388451, 16]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3154, 4194303, F3, 2, 15) (dual of [(4194303, 2), 8388452, 16]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3150, 4194301, F3, 2, 15) (dual of [(4194301, 2), 8388452, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3150, 8388602, F3, 15) (dual of [8388602, 8388452, 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 2-folding [i] based on linear OA(3150, 8388602, F3, 15) (dual of [8388602, 8388452, 16]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(3150, 4194301, F3, 2, 15) (dual of [(4194301, 2), 8388452, 16]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3154, 4194303, F3, 2, 15) (dual of [(4194303, 2), 8388452, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3155, 4194303, F3, 2, 15) (dual of [(4194303, 2), 8388451, 16]-NRT-code), using
(140, 140+15, large)-Net in Base 3 — Upper bound on s
There is no (140, 155, large)-net in base 3, because
- 13 times m-reduction [i] would yield (140, 142, large)-net in base 3, but