Best Known (18, 18+6, s)-Nets in Base 5
(18, 18+6, 2604)-Net over F5 — Constructive and digital
Digital (18, 24, 2604)-net over F5, using
- net defined by OOA [i] based on linear OOA(524, 2604, F5, 6, 6) (dual of [(2604, 6), 15600, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(524, 7812, F5, 6) (dual of [7812, 7788, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(524, 7813, F5, 6) (dual of [7813, 7789, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(524, 7812, F5, 6) (dual of [7812, 7788, 7]-code), using
(18, 18+6, 5780)-Net over F5 — Digital
Digital (18, 24, 5780)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(524, 5780, F5, 6) (dual of [5780, 5756, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(524, 7813, F5, 6) (dual of [7813, 7789, 7]-code), using
(18, 18+6, 177451)-Net in Base 5 — Upper bound on s
There is no (18, 24, 177452)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 59605 216224 936625 > 524 [i]