Best Known (221, 236, s)-Nets in Base 4
(221, 236, 7589689)-Net over F4 — Constructive and digital
Digital (221, 236, 7589689)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (57, 64, 2796205)-net over F4, using
- net defined by OOA [i] based on linear OOA(464, 2796205, F4, 9, 7) (dual of [(2796205, 9), 25165781, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(464, 2796206, F4, 3, 7) (dual of [(2796206, 3), 8388554, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(43, 5, F4, 3, 3) (dual of [(5, 3), 12, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;12,4) [i]
- linear OOA(461, 2796201, F4, 3, 7) (dual of [(2796201, 3), 8388542, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(461, large, F4, 7) (dual of [large, large−61, 8]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OOA 3-folding [i] based on linear OA(461, large, F4, 7) (dual of [large, large−61, 8]-code), using
- linear OOA(43, 5, F4, 3, 3) (dual of [(5, 3), 12, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(464, 2796206, F4, 3, 7) (dual of [(2796206, 3), 8388554, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(464, 2796205, F4, 9, 7) (dual of [(2796205, 9), 25165781, 8]-NRT-code), 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 (57, 64, 2796205)-net over F4, using
(221, 236, large)-Net over F4 — Digital
Digital (221, 236, large)-net over F4, using
- t-expansion [i] based on digital (213, 236, large)-net over F4, using
- 1 times m-reduction [i] based on digital (213, 237, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4237, large, F4, 24) (dual of [large, large−237, 25]-code), using
- 21 times code embedding in larger space [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 21 times code embedding in larger space [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4237, large, F4, 24) (dual of [large, large−237, 25]-code), using
- 1 times m-reduction [i] based on digital (213, 237, large)-net over F4, using
(221, 236, large)-Net in Base 4 — Upper bound on s
There is no (221, 236, large)-net in base 4, because
- 13 times m-reduction [i] would yield (221, 223, large)-net in base 4, but