Best Known (78−28, 78, s)-Nets in Base 27
(78−28, 78, 702)-Net over F27 — Constructive and digital
Digital (50, 78, 702)-net over F27, using
- net defined by OOA [i] based on linear OOA(2778, 702, F27, 28, 28) (dual of [(702, 28), 19578, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2778, 9828, F27, 28) (dual of [9828, 9750, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2778, 9841, F27, 28) (dual of [9841, 9763, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2778, 9828, F27, 28) (dual of [9828, 9750, 29]-code), using
(78−28, 78, 7024)-Net over F27 — Digital
Digital (50, 78, 7024)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2778, 7024, F27, 28) (dual of [7024, 6946, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2778, 9841, F27, 28) (dual of [9841, 9763, 29]-code), using
(78−28, 78, large)-Net in Base 27 — Upper bound on s
There is no (50, 78, large)-net in base 27, because
- 26 times m-reduction [i] would yield (50, 52, large)-net in base 27, but