Best Known (49−16, 49, s)-Nets in Base 27
(49−16, 49, 2462)-Net over F27 — Constructive and digital
Digital (33, 49, 2462)-net over F27, using
- net defined by OOA [i] based on linear OOA(2749, 2462, F27, 16, 16) (dual of [(2462, 16), 39343, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2749, 19696, F27, 16) (dual of [19696, 19647, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2749, 19698, F27, 16) (dual of [19698, 19649, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(2746, 19683, F27, 16) (dual of [19683, 19637, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2734, 19683, F27, 12) (dual of [19683, 19649, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(273, 15, F27, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(2749, 19698, F27, 16) (dual of [19698, 19649, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2749, 19696, F27, 16) (dual of [19696, 19647, 17]-code), using
(49−16, 49, 18787)-Net over F27 — Digital
Digital (33, 49, 18787)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2749, 18787, F27, 16) (dual of [18787, 18738, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2749, 19698, F27, 16) (dual of [19698, 19649, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(2746, 19683, F27, 16) (dual of [19683, 19637, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2734, 19683, F27, 12) (dual of [19683, 19649, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(273, 15, F27, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(2749, 19698, F27, 16) (dual of [19698, 19649, 17]-code), using
(49−16, 49, large)-Net in Base 27 — Upper bound on s
There is no (33, 49, large)-net in base 27, because
- 14 times m-reduction [i] would yield (33, 35, large)-net in base 27, but