Best Known (69, 106, s)-Nets in Base 27
(69, 106, 1093)-Net over F27 — Constructive and digital
Digital (69, 106, 1093)-net over F27, using
- net defined by OOA [i] based on linear OOA(27106, 1093, F27, 37, 37) (dual of [(1093, 37), 40335, 38]-NRT-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(27106, 19675, F27, 37) (dual of [19675, 19569, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(27106, 19683, F27, 37) (dual of [19683, 19577, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- discarding factors / shortening the dual code based on linear OA(27106, 19683, F27, 37) (dual of [19683, 19577, 38]-code), using
- OOA 18-folding and stacking with additional row [i] based on linear OA(27106, 19675, F27, 37) (dual of [19675, 19569, 38]-code), using
(69, 106, 10511)-Net over F27 — Digital
Digital (69, 106, 10511)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(27106, 10511, F27, 37) (dual of [10511, 10405, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(27106, 19683, F27, 37) (dual of [19683, 19577, 38]-code), using
- an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- discarding factors / shortening the dual code based on linear OA(27106, 19683, F27, 37) (dual of [19683, 19577, 38]-code), using
(69, 106, large)-Net in Base 27 — Upper bound on s
There is no (69, 106, large)-net in base 27, because
- 35 times m-reduction [i] would yield (69, 71, large)-net in base 27, but