Best Known (16, 16+6, s)-Nets in Base 27
(16, 16+6, 177150)-Net over F27 — Constructive and digital
Digital (16, 22, 177150)-net over F27, using
- net defined by OOA [i] based on linear OOA(2722, 177150, F27, 6, 6) (dual of [(177150, 6), 1062878, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2722, 531450, F27, 6) (dual of [531450, 531428, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(2721, 531441, F27, 6) (dual of [531441, 531420, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2713, 531441, F27, 4) (dual of [531441, 531428, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(271, 9, F27, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- OA 3-folding and stacking [i] based on linear OA(2722, 531450, F27, 6) (dual of [531450, 531428, 7]-code), using
(16, 16+6, 531451)-Net over F27 — Digital
Digital (16, 22, 531451)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2722, 531451, F27, 6) (dual of [531451, 531429, 7]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(2721, 531441, F27, 6) (dual of [531441, 531420, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2713, 531441, F27, 4) (dual of [531441, 531428, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(279, 10, F27, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,27)), using
- dual of repetition code with length 10 [i]
- linear OA(271, 10, F27, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- Reed–Solomon code RS(26,27) [i]
- discarding factors / shortening the dual code based on linear OA(271, 27, F27, 1) (dual of [27, 26, 2]-code), using
- construction X4 applied to Ce(5) ⊂ Ce(3) [i] based on
(16, 16+6, large)-Net in Base 27 — Upper bound on s
There is no (16, 22, large)-net in base 27, because
- 4 times m-reduction [i] would yield (16, 18, large)-net in base 27, but