Best Known (9−5, 9, s)-Nets in Base 27
(9−5, 9, 379)-Net over F27 — Constructive and digital
Digital (4, 9, 379)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 28)-net over F27, using
- digital (2, 7, 351)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- net defined by OOA [i] based on linear OOA(277, 351, F27, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
(9−5, 9, 458)-Net over F27 — Digital
Digital (4, 9, 458)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(279, 458, F27, 5) (dual of [458, 449, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(279, 728, F27, 5) (dual of [728, 719, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(279, 728, F27, 5) (dual of [728, 719, 6]-code), using
(9−5, 9, 28906)-Net in Base 27 — Upper bound on s
There is no (4, 9, 28907)-net in base 27, because
- 1 times m-reduction [i] would yield (4, 8, 28907)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 282449 025093 > 278 [i]