Best Known (37, 45, s)-Nets in Base 3
(37, 45, 2460)-Net over F3 — Constructive and digital
Digital (37, 45, 2460)-net over F3, using
- net defined by OOA [i] based on linear OOA(345, 2460, F3, 8, 8) (dual of [(2460, 8), 19635, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(345, 9840, F3, 8) (dual of [9840, 9795, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(345, 9841, F3, 8) (dual of [9841, 9796, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(345, 9840, F3, 8) (dual of [9840, 9795, 9]-code), using
(37, 45, 4920)-Net over F3 — Digital
Digital (37, 45, 4920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(345, 4920, F3, 2, 8) (dual of [(4920, 2), 9795, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(345, 9840, F3, 8) (dual of [9840, 9795, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(345, 9841, F3, 8) (dual of [9841, 9796, 9]-code), using
- OOA 2-folding [i] based on linear OA(345, 9840, F3, 8) (dual of [9840, 9795, 9]-code), using
(37, 45, 258006)-Net in Base 3 — Upper bound on s
There is no (37, 45, 258007)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2954 324950 781742 534777 > 345 [i]