Best Known (89, 107, s)-Nets in Base 3
(89, 107, 1093)-Net over F3 — Constructive and digital
Digital (89, 107, 1093)-net over F3, using
- net defined by OOA [i] based on linear OOA(3107, 1093, F3, 18, 18) (dual of [(1093, 18), 19567, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3107, 9837, F3, 18) (dual of [9837, 9730, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3107, 9840, F3, 18) (dual of [9840, 9733, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(3107, 9837, F3, 18) (dual of [9837, 9730, 19]-code), using
(89, 107, 4920)-Net over F3 — Digital
Digital (89, 107, 4920)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3107, 4920, F3, 2, 18) (dual of [(4920, 2), 9733, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3107, 9840, F3, 18) (dual of [9840, 9733, 19]-code), using
(89, 107, 975347)-Net in Base 3 — Upper bound on s
There is no (89, 107, 975348)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1127 138724 762245 236438 721607 010294 031950 397203 272169 > 3107 [i]