Best Known (114, 114+10, s)-Nets in Base 5
(114, 114+10, 3550751)-Net over F5 — Constructive and digital
Digital (114, 124, 3550751)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (27, 32, 195311)-net over F5, using
- net defined by OOA [i] based on linear OOA(532, 195311, F5, 5, 5) (dual of [(195311, 5), 976523, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(532, 390623, F5, 5) (dual of [390623, 390591, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(532, 390624, F5, 5) (dual of [390624, 390592, 6]-code), using
- 1 times truncation [i] based on linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- 1 times truncation [i] based on linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(532, 390624, F5, 5) (dual of [390624, 390592, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(532, 390623, F5, 5) (dual of [390623, 390591, 6]-code), using
- net defined by OOA [i] based on linear OOA(532, 195311, F5, 5, 5) (dual of [(195311, 5), 976523, 6]-NRT-code), using
- digital (82, 92, 3355440)-net over F5, using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F25, using
- digital (27, 32, 195311)-net over F5, using
(114, 114+10, large)-Net over F5 — Digital
Digital (114, 124, large)-net over F5, using
- t-expansion [i] based on digital (112, 124, large)-net over F5, using
- 3 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
- 3 times m-reduction [i] based on digital (112, 127, large)-net over F5, using
(114, 114+10, large)-Net in Base 5 — Upper bound on s
There is no (114, 124, large)-net in base 5, because
- 8 times m-reduction [i] would yield (114, 116, large)-net in base 5, but