Best Known (59, 91, s)-Nets in Base 27
(59, 91, 1230)-Net over F27 — Constructive and digital
Digital (59, 91, 1230)-net over F27, using
- net defined by OOA [i] based on linear OOA(2791, 1230, F27, 32, 32) (dual of [(1230, 32), 39269, 33]-NRT-code), using
- OA 16-folding and stacking [i] based on linear OA(2791, 19680, F27, 32) (dual of [19680, 19589, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2791, 19683, F27, 32) (dual of [19683, 19592, 33]-code), using
- an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- discarding factors / shortening the dual code based on linear OA(2791, 19683, F27, 32) (dual of [19683, 19592, 33]-code), using
- OA 16-folding and stacking [i] based on linear OA(2791, 19680, F27, 32) (dual of [19680, 19589, 33]-code), using
(59, 91, 9843)-Net over F27 — Digital
Digital (59, 91, 9843)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2791, 9843, F27, 2, 32) (dual of [(9843, 2), 19595, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2791, 19686, F27, 32) (dual of [19686, 19595, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- linear OA(2791, 19683, F27, 32) (dual of [19683, 19592, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2788, 19683, F27, 31) (dual of [19683, 19595, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(31) ⊂ Ce(30) [i] based on
- OOA 2-folding [i] based on linear OA(2791, 19686, F27, 32) (dual of [19686, 19595, 33]-code), using
(59, 91, large)-Net in Base 27 — Upper bound on s
There is no (59, 91, large)-net in base 27, because
- 30 times m-reduction [i] would yield (59, 61, large)-net in base 27, but