Best Known (97, 117, s)-Nets in Base 3
(97, 117, 984)-Net over F3 — Constructive and digital
Digital (97, 117, 984)-net over F3, using
- net defined by OOA [i] based on linear OOA(3117, 984, F3, 20, 20) (dual of [(984, 20), 19563, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3117, 9840, F3, 20) (dual of [9840, 9723, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3117, 9841, F3, 20) (dual of [9841, 9724, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3117, 9840, F3, 20) (dual of [9840, 9723, 21]-code), using
(97, 117, 4920)-Net over F3 — Digital
Digital (97, 117, 4920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3117, 4920, F3, 2, 20) (dual of [(4920, 2), 9723, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3117, 9840, F3, 20) (dual of [9840, 9723, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3117, 9841, F3, 20) (dual of [9841, 9724, 21]-code), using
- OOA 2-folding [i] based on linear OA(3117, 9840, F3, 20) (dual of [9840, 9723, 21]-code), using
(97, 117, 865486)-Net in Base 3 — Upper bound on s
There is no (97, 117, 865487)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 66 556439 845848 879443 908840 650243 037654 165516 804646 858637 > 3117 [i]