Best Known (66, 66+18, s)-Nets in Base 5
(66, 66+18, 868)-Net over F5 — Constructive and digital
Digital (66, 84, 868)-net over F5, using
- net defined by OOA [i] based on linear OOA(584, 868, F5, 18, 18) (dual of [(868, 18), 15540, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(584, 7812, F5, 18) (dual of [7812, 7728, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(584, 7813, F5, 18) (dual of [7813, 7729, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(584, 7812, F5, 18) (dual of [7812, 7728, 19]-code), using
(66, 66+18, 7173)-Net over F5 — Digital
Digital (66, 84, 7173)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(584, 7173, F5, 18) (dual of [7173, 7089, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(584, 7813, F5, 18) (dual of [7813, 7729, 19]-code), using
(66, 66+18, 3462666)-Net in Base 5 — Upper bound on s
There is no (66, 84, 3462667)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 51698 804025 070183 867046 822272 158122 850952 673675 491186 063885 > 584 [i]