Best Known (115, 115+15, s)-Nets in Base 5
(115, 115+15, 1198396)-Net over F5 — Constructive and digital
Digital (115, 130, 1198396)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 25)-net over F5, using
- digital (105, 120, 1198371)-net over F5, using
- net defined by OOA [i] based on linear OOA(5120, 1198371, F5, 15, 15) (dual of [(1198371, 15), 17975445, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(5120, 8388598, F5, 15) (dual of [8388598, 8388478, 16]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(5120, large, F5, 15) (dual of [large, large−120, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(5120, 8388598, F5, 15) (dual of [8388598, 8388478, 16]-code), using
- net defined by OOA [i] based on linear OOA(5120, 1198371, F5, 15, 15) (dual of [(1198371, 15), 17975445, 16]-NRT-code), using
(115, 115+15, large)-Net over F5 — Digital
Digital (115, 130, large)-net over F5, using
- 53 times duplication [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
(115, 115+15, large)-Net in Base 5 — Upper bound on s
There is no (115, 130, large)-net in base 5, because
- 13 times m-reduction [i] would yield (115, 117, large)-net in base 5, but