Best Known (6, 11, s)-Nets in Base 27
(6, 11, 1054)-Net over F27 — Constructive and digital
Digital (6, 11, 1054)-net over F27, using
- net defined by OOA [i] based on linear OOA(2711, 1054, F27, 5, 5) (dual of [(1054, 5), 5259, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2711, 2109, F27, 5) (dual of [2109, 2098, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(271, 703, F27, 1) (dual of [703, 702, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(273, 703, F27, 2) (dual of [703, 700, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using
- linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- linear OA(271, 703, F27, 1) (dual of [703, 702, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(2711, 2109, F27, 5) (dual of [2109, 2098, 6]-code), using
(6, 11, 2109)-Net over F27 — Digital
Digital (6, 11, 2109)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2711, 2109, F27, 5) (dual of [2109, 2098, 6]-code), using
- (u, u−v, u+v+w)-construction [i] based on
- linear OA(271, 703, F27, 1) (dual of [703, 702, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(273, 703, F27, 2) (dual of [703, 700, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using
- linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- linear OA(271, 703, F27, 1) (dual of [703, 702, 2]-code), using
- (u, u−v, u+v+w)-construction [i] based on
(6, 11, 3240)-Net in Base 27 — Constructive
(6, 11, 3240)-net in base 27, using
- 271 times duplication [i] based on (5, 10, 3240)-net in base 27, using
- net defined by OOA [i] based on OOA(2710, 3240, S27, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(2710, 6481, S27, 5), using
- discarding parts of the base [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on OA(2710, 6481, S27, 5), using
- net defined by OOA [i] based on OOA(2710, 3240, S27, 5, 5), using
(6, 11, 780477)-Net in Base 27 — Upper bound on s
There is no (6, 11, 780478)-net in base 27, because
- 1 times m-reduction [i] would yield (6, 10, 780478)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 205 891621 454013 > 2710 [i]