Best Known (237−18, 237, s)-Nets in Base 3
(237−18, 237, 1062895)-Net over F3 — Constructive and digital
Digital (219, 237, 1062895)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 13)-net over F3, using
- digital (206, 224, 1062882)-net over F3, using
- trace code for nets [i] based on digital (94, 112, 531441)-net over F9, using
- net defined by OOA [i] based on linear OOA(9112, 531441, F9, 18, 18) (dual of [(531441, 18), 9565826, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9112, 4782969, F9, 18) (dual of [4782969, 4782857, 19]-code), using
- 1 times truncation [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(9113, 4782970, F9, 19) (dual of [4782970, 4782857, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(9112, 4782969, F9, 18) (dual of [4782969, 4782857, 19]-code), using
- net defined by OOA [i] based on linear OOA(9112, 531441, F9, 18, 18) (dual of [(531441, 18), 9565826, 19]-NRT-code), using
- trace code for nets [i] based on digital (94, 112, 531441)-net over F9, using
(237−18, 237, large)-Net over F3 — Digital
Digital (219, 237, large)-net over F3, using
- 39 times duplication [i] based on digital (210, 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
(237−18, 237, large)-Net in Base 3 — Upper bound on s
There is no (219, 237, large)-net in base 3, because
- 16 times m-reduction [i] would yield (219, 221, large)-net in base 3, but