Best Known (46, 70, s)-Nets in Base 27
(46, 70, 1640)-Net over F27 — Constructive and digital
Digital (46, 70, 1640)-net over F27, using
- net defined by OOA [i] based on linear OOA(2770, 1640, F27, 24, 24) (dual of [(1640, 24), 39290, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2770, 19680, F27, 24) (dual of [19680, 19610, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2770, 19680, F27, 24) (dual of [19680, 19610, 25]-code), using
(46, 70, 10733)-Net over F27 — Digital
Digital (46, 70, 10733)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2770, 10733, F27, 24) (dual of [10733, 10663, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using
(46, 70, large)-Net in Base 27 — Upper bound on s
There is no (46, 70, large)-net in base 27, because
- 22 times m-reduction [i] would yield (46, 48, large)-net in base 27, but