Best Known (48, 72, s)-Nets in Base 27
(48, 72, 1641)-Net over F27 — Constructive and digital
Digital (48, 72, 1641)-net over F27, using
- net defined by OOA [i] based on linear OOA(2772, 1641, F27, 24, 24) (dual of [(1641, 24), 39312, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2772, 19692, F27, 24) (dual of [19692, 19620, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2772, 19694, F27, 24) (dual of [19694, 19622, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2761, 19683, F27, 21) (dual of [19683, 19622, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(272, 11, F27, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2772, 19694, F27, 24) (dual of [19694, 19622, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2772, 19692, F27, 24) (dual of [19692, 19620, 25]-code), using
(48, 72, 14486)-Net over F27 — Digital
Digital (48, 72, 14486)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2772, 14486, F27, 24) (dual of [14486, 14414, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2772, 19694, F27, 24) (dual of [19694, 19622, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- linear OA(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2761, 19683, F27, 21) (dual of [19683, 19622, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(272, 11, F27, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,27)), using
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- Reed–Solomon code RS(25,27) [i]
- discarding factors / shortening the dual code based on linear OA(272, 27, F27, 2) (dual of [27, 25, 3]-code or 27-arc in PG(1,27)), using
- construction X applied to Ce(23) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2772, 19694, F27, 24) (dual of [19694, 19622, 25]-code), using
(48, 72, large)-Net in Base 27 — Upper bound on s
There is no (48, 72, large)-net in base 27, because
- 22 times m-reduction [i] would yield (48, 50, large)-net in base 27, but