Best Known (19, 24, s)-Nets in Base 5
(19, 24, 7811)-Net over F5 — Constructive and digital
Digital (19, 24, 7811)-net over F5, using
- net defined by OOA [i] based on linear OOA(524, 7811, F5, 5, 5) (dual of [(7811, 5), 39031, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(524, 15623, F5, 5) (dual of [15623, 15599, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(524, 15624, F5, 5) (dual of [15624, 15600, 6]-code), using
- the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(524, 15624, F5, 5) (dual of [15624, 15600, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(524, 15623, F5, 5) (dual of [15623, 15599, 6]-code), using
(19, 24, 15624)-Net over F5 — Digital
Digital (19, 24, 15624)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(524, 15624, F5, 5) (dual of [15624, 15600, 6]-code), using
- the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
(19, 24, large)-Net in Base 5 — Upper bound on s
There is no (19, 24, large)-net in base 5, because
- 3 times m-reduction [i] would yield (19, 21, large)-net in base 5, but