Best Known (110, 120, s)-Nets in Base 5
(110, 120, 3394501)-Net over F5 — Constructive and digital
Digital (110, 120, 3394501)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (23, 28, 39061)-net over F5, using
- net defined by OOA [i] based on linear OOA(528, 39061, F5, 5, 5) (dual of [(39061, 5), 195277, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(528, 78123, F5, 5) (dual of [78123, 78095, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(528, 78124, F5, 5) (dual of [78124, 78096, 6]-code), using
- 1 times truncation [i] based on linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- 1 times truncation [i] based on linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(528, 78124, F5, 5) (dual of [78124, 78096, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(528, 78123, F5, 5) (dual of [78123, 78095, 6]-code), using
- net defined by OOA [i] based on linear OOA(528, 39061, F5, 5, 5) (dual of [(39061, 5), 195277, 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 (23, 28, 39061)-net over F5, using
(110, 120, large)-Net over F5 — Digital
Digital (110, 120, large)-net over F5, using
- 52 times duplication [i] based on digital (108, 118, large)-net over F5, using
- t-expansion [i] based on digital (104, 118, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5118, large, F5, 14) (dual of [large, large−118, 15]-code), using
- 7 times code embedding in larger space [i] based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- 7 times code embedding in larger space [i] based on linear OA(5111, large, F5, 14) (dual of [large, large−111, 15]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(5118, large, F5, 14) (dual of [large, large−118, 15]-code), using
- t-expansion [i] based on digital (104, 118, large)-net over F5, using
(110, 120, large)-Net in Base 5 — Upper bound on s
There is no (110, 120, large)-net in base 5, because
- 8 times m-reduction [i] would yield (110, 112, large)-net in base 5, but