Best Known (54−19, 54, s)-Nets in Base 27
(54−19, 54, 1093)-Net over F27 — Constructive and digital
Digital (35, 54, 1093)-net over F27, using
- net defined by OOA [i] based on linear OOA(2754, 1093, F27, 19, 19) (dual of [(1093, 19), 20713, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2754, 9838, F27, 19) (dual of [9838, 9784, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2754, 9841, F27, 19) (dual of [9841, 9787, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2754, 9838, F27, 19) (dual of [9838, 9784, 20]-code), using
(54−19, 54, 7999)-Net over F27 — Digital
Digital (35, 54, 7999)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2754, 7999, F27, 19) (dual of [7999, 7945, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2754, 9841, F27, 19) (dual of [9841, 9787, 20]-code), using
(54−19, 54, large)-Net in Base 27 — Upper bound on s
There is no (35, 54, large)-net in base 27, because
- 17 times m-reduction [i] would yield (35, 37, large)-net in base 27, but