Best Known (93−10, 93, s)-Nets in Base 5
(93−10, 93, 3355440)-Net over F5 — Constructive and digital
Digital (83, 93, 3355440)-net over F5, using
- 51 times duplication [i] based on 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
(93−10, 93, large)-Net over F5 — Digital
Digital (83, 93, large)-net over F5, using
- 53 times duplication [i] based on digital (80, 90, large)-net over F5, using
- t-expansion [i] based on digital (79, 90, large)-net over F5, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(590, large, F5, 11) (dual of [large, large−90, 12]-code), using
- 9 times code embedding in larger space [i] based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 520−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- 9 times code embedding in larger space [i] based on linear OA(581, large, F5, 11) (dual of [large, large−81, 12]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(590, large, F5, 11) (dual of [large, large−90, 12]-code), using
- t-expansion [i] based on digital (79, 90, large)-net over F5, using
(93−10, 93, large)-Net in Base 5 — Upper bound on s
There is no (83, 93, large)-net in base 5, because
- 8 times m-reduction [i] would yield (83, 85, large)-net in base 5, but