Best Known (83, 91, s)-Nets in Base 4
(83, 91, 8388600)-Net over F4 — Constructive and digital
Digital (83, 91, 8388600)-net over F4, using
- 43 times duplication [i] based on digital (80, 88, 8388600)-net over F4, using
- trace code for nets [i] based on digital (36, 44, 4194300)-net over F16, using
- net defined by OOA [i] based on linear OOA(1644, 4194300, F16, 10, 8) (dual of [(4194300, 10), 41942956, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(1644, 8388601, F16, 2, 8) (dual of [(8388601, 2), 16777158, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1644, 8388602, F16, 2, 8) (dual of [(8388602, 2), 16777160, 9]-NRT-code), using
- trace code [i] based on linear OOA(25622, 4194301, F256, 2, 8) (dual of [(4194301, 2), 8388580, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25622, 8388602, F256, 8) (dual of [8388602, 8388580, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(25622, large, F256, 8) (dual of [large, large−22, 9]-code), using
- OOA 2-folding [i] based on linear OA(25622, 8388602, F256, 8) (dual of [8388602, 8388580, 9]-code), using
- trace code [i] based on linear OOA(25622, 4194301, F256, 2, 8) (dual of [(4194301, 2), 8388580, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1644, 8388602, F16, 2, 8) (dual of [(8388602, 2), 16777160, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(1644, 8388601, F16, 2, 8) (dual of [(8388601, 2), 16777158, 9]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1644, 4194300, F16, 10, 8) (dual of [(4194300, 10), 41942956, 9]-NRT-code), using
- trace code for nets [i] based on digital (36, 44, 4194300)-net over F16, using
(83, 91, large)-Net over F4 — Digital
Digital (83, 91, large)-net over F4, using
- t-expansion [i] based on digital (82, 91, large)-net over F4, using
- 1 times m-reduction [i] based on digital (82, 92, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(492, large, F4, 10) (dual of [large, large−92, 11]-code), using
- 7 times code embedding in larger space [i] based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 7 times code embedding in larger space [i] based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(492, large, F4, 10) (dual of [large, large−92, 11]-code), using
- 1 times m-reduction [i] based on digital (82, 92, large)-net over F4, using
(83, 91, large)-Net in Base 4 — Upper bound on s
There is no (83, 91, large)-net in base 4, because
- 6 times m-reduction [i] would yield (83, 85, large)-net in base 4, but