Best Known (194−15, 194, s)-Nets in Base 4
(194−15, 194, 4793679)-Net over F4 — Constructive and digital
Digital (179, 194, 4793679)-net over F4, using
- 41 times duplication [i] based on digital (178, 193, 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 (157, 172, 4793484)-net over F4, using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(25643, large, F256, 15) (dual of [large, large−43, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(25643, 8388598, F256, 15) (dual of [8388598, 8388555, 16]-code), using
- net defined by OOA [i] based on linear OOA(25643, 1198371, F256, 15, 15) (dual of [(1198371, 15), 17975522, 16]-NRT-code), using
- trace code for nets [i] based on digital (28, 43, 1198371)-net over F256, using
- digital (14, 21, 195)-net over F4, using
- (u, u+v)-construction [i] based on
(194−15, 194, large)-Net over F4 — Digital
Digital (179, 194, large)-net over F4, using
- t-expansion [i] based on digital (177, 194, large)-net over F4, using
- 3 times m-reduction [i] based on digital (177, 197, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4197, large, F4, 20) (dual of [large, large−197, 21]-code), using
- 17 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 17 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4197, large, F4, 20) (dual of [large, large−197, 21]-code), using
- 3 times m-reduction [i] based on digital (177, 197, large)-net over F4, using
(194−15, 194, large)-Net in Base 4 — Upper bound on s
There is no (179, 194, large)-net in base 4, because
- 13 times m-reduction [i] would yield (179, 181, large)-net in base 4, but