Best Known (151, 151+15, s)-Nets in Base 3
(151, 151+15, 1198405)-Net over F3 — Constructive and digital
Digital (151, 166, 1198405)-net over F3, using
- 32 times duplication [i] based on digital (149, 164, 1198405)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (7, 14, 34)-net over F3, using
- 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
- (u, u+v)-construction [i] based on
(151, 151+15, 4194342)-Net over F3 — Digital
Digital (151, 166, 4194342)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3166, 4194342, F3, 2, 15) (dual of [(4194342, 2), 8388518, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(316, 41, F3, 2, 7) (dual of [(41, 2), 66, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-code), using
- 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
- linear OOA(316, 41, F3, 2, 7) (dual of [(41, 2), 66, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(151, 151+15, large)-Net in Base 3 — Upper bound on s
There is no (151, 166, large)-net in base 3, because
- 13 times m-reduction [i] would yield (151, 153, large)-net in base 3, but