Best Known (215, 215+14, s)-Nets in Base 3
(215, 215+14, 4793524)-Net over F3 — Constructive and digital
Digital (215, 229, 4793524)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (10, 17, 40)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 5, 20)-net over F3, using
- net defined by OOA [i] based on linear OOA(35, 20, F3, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(35, 20, F3, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(35, 20, F3, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
- digital (5, 12, 20)-net over F3, using
- digital (2, 5, 20)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (198, 212, 4793484)-net over F3, using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F81, using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(8153, large, F81, 14) (dual of [large, large−53, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(8153, 8388597, F81, 14) (dual of [8388597, 8388544, 15]-code), using
- net defined by OOA [i] based on linear OOA(8153, 1198371, F81, 14, 14) (dual of [(1198371, 14), 16777141, 15]-NRT-code), using
- trace code for nets [i] based on digital (39, 53, 1198371)-net over F81, using
- digital (10, 17, 40)-net over F3, using
(215, 215+14, large)-Net over F3 — Digital
Digital (215, 229, large)-net over F3, using
- 31 times duplication [i] based on digital (214, 228, large)-net over F3, using
- t-expansion [i] based on digital (209, 228, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3228, large, F3, 19) (dual of [large, large−228, 20]-code), using
- 47 times code embedding in larger space [i] based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 47 times code embedding in larger space [i] based on linear OA(3181, large, F3, 19) (dual of [large, large−181, 20]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3228, large, F3, 19) (dual of [large, large−228, 20]-code), using
- t-expansion [i] based on digital (209, 228, large)-net over F3, using
(215, 215+14, large)-Net in Base 3 — Upper bound on s
There is no (215, 229, large)-net in base 3, because
- 12 times m-reduction [i] would yield (215, 217, large)-net in base 3, but