Best Known (89, 89+19, s)-Nets in Base 3
(89, 89+19, 1093)-Net over F3 — Constructive and digital
Digital (89, 108, 1093)-net over F3, using
- net defined by OOA [i] based on linear OOA(3108, 1093, F3, 19, 19) (dual of [(1093, 19), 20659, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3108, 9838, F3, 19) (dual of [9838, 9730, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3108, 9841, F3, 19) (dual of [9841, 9733, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3108, 9838, F3, 19) (dual of [9838, 9730, 20]-code), using
(89, 89+19, 4910)-Net over F3 — Digital
Digital (89, 108, 4910)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3108, 4910, F3, 2, 19) (dual of [(4910, 2), 9712, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3108, 4920, F3, 2, 19) (dual of [(4920, 2), 9732, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3108, 9840, F3, 19) (dual of [9840, 9732, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3108, 9841, F3, 19) (dual of [9841, 9733, 20]-code), using
- OOA 2-folding [i] based on linear OA(3108, 9840, F3, 19) (dual of [9840, 9732, 20]-code), using
- discarding factors / shortening the dual code based on linear OOA(3108, 4920, F3, 2, 19) (dual of [(4920, 2), 9732, 20]-NRT-code), using
(89, 89+19, 975347)-Net in Base 3 — Upper bound on s
There is no (89, 108, 975348)-net in base 3, because
- 1 times m-reduction [i] would yield (89, 107, 975348)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1127 138724 762245 236438 721607 010294 031950 397203 272169 > 3107 [i]