Best Known (102, 102+9, s)-Nets in Base 3
(102, 102+9, 2391483)-Net over F3 — Constructive and digital
Digital (102, 111, 2391483)-net over F3, using
- net defined by OOA [i] based on linear OOA(3111, 2391483, F3, 12, 9) (dual of [(2391483, 12), 28697685, 10]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(3111, 2391484, F3, 4, 9) (dual of [(2391484, 4), 9565825, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(327, 1594322, F3, 4, 4) (dual of [(1594322, 4), 6377261, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(327, 1594322, F3, 3, 4) (dual of [(1594322, 3), 4782939, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (23, 27, 1594322)-net over F3, using
- appending kth column [i] based on linear OOA(327, 1594322, F3, 3, 4) (dual of [(1594322, 3), 4782939, 5]-NRT-code), using
- linear OOA(384, 1195742, F3, 4, 9) (dual of [(1195742, 4), 4782884, 10]-NRT-code), using
- OOA 4-folding [i] based on linear OA(384, 4782968, F3, 9) (dual of [4782968, 4782884, 10]-code), using
- 1 times truncation [i] based on linear OA(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 1 times truncation [i] based on linear OA(385, 4782969, F3, 10) (dual of [4782969, 4782884, 11]-code), using
- OOA 4-folding [i] based on linear OA(384, 4782968, F3, 9) (dual of [4782968, 4782884, 10]-code), using
- linear OOA(327, 1594322, F3, 4, 4) (dual of [(1594322, 4), 6377261, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(3111, 2391484, F3, 4, 9) (dual of [(2391484, 4), 9565825, 10]-NRT-code), using
(102, 102+9, large)-Net over F3 — Digital
Digital (102, 111, large)-net over F3, using
- 311 times duplication [i] based on digital (91, 100, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3100, large, F3, 9) (dual of [large, large−100, 10]-code), using
- 10 times code embedding in larger space [i] based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- 10 times code embedding in larger space [i] based on linear OA(390, large, F3, 9) (dual of [large, large−90, 10]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3100, large, F3, 9) (dual of [large, large−100, 10]-code), using
(102, 102+9, large)-Net in Base 3 — Upper bound on s
There is no (102, 111, large)-net in base 3, because
- 7 times m-reduction [i] would yield (102, 104, large)-net in base 3, but