Best Known (114, 114+12, s)-Nets in Base 5
(114, 114+12, 2796259)-Net over F5 — Constructive and digital
Digital (114, 126, 2796259)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (8, 14, 59)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (100, 112, 2796200)-net over F5, using
- net defined by OOA [i] based on linear OOA(5112, 2796200, F5, 14, 12) (dual of [(2796200, 14), 39146688, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(5112, 8388601, F5, 2, 12) (dual of [(8388601, 2), 16777090, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5112, 8388602, F5, 2, 12) (dual of [(8388602, 2), 16777092, 13]-NRT-code), using
- trace code [i] based on linear OOA(2556, 4194301, F25, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2556, 8388602, F25, 12) (dual of [8388602, 8388546, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2556, large, F25, 12) (dual of [large, large−56, 13]-code), using
- OOA 2-folding [i] based on linear OA(2556, 8388602, F25, 12) (dual of [8388602, 8388546, 13]-code), using
- trace code [i] based on linear OOA(2556, 4194301, F25, 2, 12) (dual of [(4194301, 2), 8388546, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5112, 8388602, F5, 2, 12) (dual of [(8388602, 2), 16777092, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(5112, 8388601, F5, 2, 12) (dual of [(8388601, 2), 16777090, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(5112, 2796200, F5, 14, 12) (dual of [(2796200, 14), 39146688, 13]-NRT-code), using
- digital (8, 14, 59)-net over F5, using
(114, 114+12, large)-Net over F5 — Digital
Digital (114, 126, large)-net over F5, using
- t-expansion [i] based on digital (112, 126, large)-net over F5, using
- 1 times m-reduction [i] based on digital (112, 127, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5127, large, F5, 15) (dual of [large, large−127, 16]-code), using
- 7 times code embedding in larger space [i] based on linear OA(5120, large, F5, 15) (dual of [large, large−120, 16]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- 7 times code embedding in larger space [i] based on linear OA(5120, large, F5, 15) (dual of [large, large−120, 16]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5127, large, F5, 15) (dual of [large, large−127, 16]-code), using
- 1 times m-reduction [i] based on digital (112, 127, large)-net over F5, using
(114, 114+12, large)-Net in Base 5 — Upper bound on s
There is no (114, 126, large)-net in base 5, because
- 10 times m-reduction [i] would yield (114, 116, large)-net in base 5, but