Best Known (49−10, 49, s)-Nets in Base 4
(49−10, 49, 1092)-Net over F4 — Constructive and digital
Digital (39, 49, 1092)-net over F4, using
- net defined by OOA [i] based on linear OOA(449, 1092, F4, 10, 10) (dual of [(1092, 10), 10871, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(449, 5460, F4, 10) (dual of [5460, 5411, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(449, 5461, F4, 10) (dual of [5461, 5412, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(449, 5460, F4, 10) (dual of [5460, 5411, 11]-code), using
(49−10, 49, 5134)-Net over F4 — Digital
Digital (39, 49, 5134)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(449, 5134, F4, 10) (dual of [5134, 5085, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(449, 5461, F4, 10) (dual of [5461, 5412, 11]-code), using
(49−10, 49, 690081)-Net in Base 4 — Upper bound on s
There is no (39, 49, 690082)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 316913 005921 024177 603689 929992 > 449 [i]