Best Known (92, 106, s)-Nets in Base 16
(92, 106, 2440433)-Net over F16 — Constructive and digital
Digital (92, 106, 2440433)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (19, 26, 43691)-net over F16, using
- net defined by OOA [i] based on linear OOA(1626, 43691, F16, 7, 7) (dual of [(43691, 7), 305811, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(1626, 131074, F16, 7) (dual of [131074, 131048, 8]-code), using
- trace code [i] based on linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- trace code [i] based on linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(1626, 131074, F16, 7) (dual of [131074, 131048, 8]-code), using
- net defined by OOA [i] based on linear OOA(1626, 43691, F16, 7, 7) (dual of [(43691, 7), 305811, 8]-NRT-code), using
- digital (66, 80, 2396742)-net over F16, using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- digital (19, 26, 43691)-net over F16, using
(92, 106, large)-Net over F16 — Digital
Digital (92, 106, large)-net over F16, using
- t-expansion [i] based on digital (89, 106, large)-net over F16, using
- 3 times m-reduction [i] based on digital (89, 109, large)-net over F16, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(16109, large, F16, 20) (dual of [large, large−109, 21]-code), using
- 3 times m-reduction [i] based on digital (89, 109, large)-net over F16, using
(92, 106, large)-Net in Base 16 — Upper bound on s
There is no (92, 106, large)-net in base 16, because
- 12 times m-reduction [i] would yield (92, 94, large)-net in base 16, but