Best Known (92−22, 92, s)-Nets in Base 27
(92−22, 92, 48316)-Net over F27 — Constructive and digital
Digital (70, 92, 48316)-net over F27, using
- net defined by OOA [i] based on linear OOA(2792, 48316, F27, 22, 22) (dual of [(48316, 22), 1062860, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2792, 531476, F27, 22) (dual of [531476, 531384, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- linear OA(2785, 531441, F27, 22) (dual of [531441, 531356, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2757, 531441, F27, 15) (dual of [531441, 531384, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(277, 35, F27, 6) (dual of [35, 28, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(277, 38, F27, 6) (dual of [38, 31, 7]-code), using
- extended algebraic-geometric code AGe(F,31P) [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- discarding factors / shortening the dual code based on linear OA(277, 38, F27, 6) (dual of [38, 31, 7]-code), using
- construction X applied to Ce(21) ⊂ Ce(14) [i] based on
- OA 11-folding and stacking [i] based on linear OA(2792, 531476, F27, 22) (dual of [531476, 531384, 23]-code), using
(92−22, 92, 622677)-Net over F27 — Digital
Digital (70, 92, 622677)-net over F27, using
(92−22, 92, large)-Net in Base 27 — Upper bound on s
There is no (70, 92, large)-net in base 27, because
- 20 times m-reduction [i] would yield (70, 72, large)-net in base 27, but