Best Known (77−27, 77, s)-Nets in Base 27
(77−27, 77, 756)-Net over F27 — Constructive and digital
Digital (50, 77, 756)-net over F27, using
- net defined by OOA [i] based on linear OOA(2777, 756, F27, 27, 27) (dual of [(756, 27), 20335, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2777, 9829, F27, 27) (dual of [9829, 9752, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2777, 9840, F27, 27) (dual of [9840, 9763, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2777, 9829, F27, 27) (dual of [9829, 9752, 28]-code), using
(77−27, 77, 8778)-Net over F27 — Digital
Digital (50, 77, 8778)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2777, 8778, F27, 27) (dual of [8778, 8701, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2777, 9840, F27, 27) (dual of [9840, 9763, 28]-code), using
(77−27, 77, large)-Net in Base 27 — Upper bound on s
There is no (50, 77, large)-net in base 27, because
- 25 times m-reduction [i] would yield (50, 52, large)-net in base 27, but