Best Known (168, 182, s)-Nets in Base 4
(168, 182, 4793679)-Net over F4 — Constructive and digital
Digital (168, 182, 4793679)-net over F4, using
- 41 times duplication [i] based on digital (167, 181, 4793679)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (14, 21, 195)-net over F4, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 7, 65)-net over F64, using
- digital (146, 160, 4793484)-net over F4, 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 (14, 21, 195)-net over F4, using
- (u, u+v)-construction [i] based on
(168, 182, large)-Net over F4 — Digital
Digital (168, 182, large)-net over F4, using
- t-expansion [i] based on digital (167, 182, large)-net over F4, using
- 4 times m-reduction [i] based on digital (167, 186, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4186, large, F4, 19) (dual of [large, large−186, 20]-code), using
- 17 times code embedding in larger space [i] based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 17 times code embedding in larger space [i] based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4186, large, F4, 19) (dual of [large, large−186, 20]-code), using
- 4 times m-reduction [i] based on digital (167, 186, large)-net over F4, using
(168, 182, large)-Net in Base 4 — Upper bound on s
There is no (168, 182, large)-net in base 4, because
- 12 times m-reduction [i] would yield (168, 170, large)-net in base 4, but