Best Known (44, 54, s)-Nets in Base 3
(44, 54, 1968)-Net over F3 — Constructive and digital
Digital (44, 54, 1968)-net over F3, using
- net defined by OOA [i] based on linear OOA(354, 1968, F3, 10, 10) (dual of [(1968, 10), 19626, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(354, 9840, F3, 10) (dual of [9840, 9786, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(354, 9841, F3, 10) (dual of [9841, 9787, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(354, 9840, F3, 10) (dual of [9840, 9786, 11]-code), using
(44, 54, 4920)-Net over F3 — Digital
Digital (44, 54, 4920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(354, 4920, F3, 2, 10) (dual of [(4920, 2), 9786, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(354, 9840, F3, 10) (dual of [9840, 9786, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(354, 9841, F3, 10) (dual of [9841, 9787, 11]-code), using
- OOA 2-folding [i] based on linear OA(354, 9840, F3, 10) (dual of [9840, 9786, 11]-code), using
(44, 54, 185227)-Net in Base 3 — Upper bound on s
There is no (44, 54, 185228)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 58 150663 306566 021439 613433 > 354 [i]