Best Known (19−5, 19, s)-Nets in Base 27
(19−5, 19, 265750)-Net over F27 — Constructive and digital
Digital (14, 19, 265750)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 28)-net over F27, using
- digital (12, 17, 265722)-net over F27, using
- net defined by OOA [i] based on linear OOA(2717, 265722, F27, 5, 5) (dual of [(265722, 5), 1328593, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2717, 531445, F27, 5) (dual of [531445, 531428, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(2717, 531441, F27, 5) (dual of [531441, 531424, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(270, 4, F27, 0) (dual of [4, 4, 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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(2717, 531445, F27, 5) (dual of [531445, 531428, 6]-code), using
- net defined by OOA [i] based on linear OOA(2717, 265722, F27, 5, 5) (dual of [(265722, 5), 1328593, 6]-NRT-code), using
(19−5, 19, 535869)-Net over F27 — Digital
Digital (14, 19, 535869)-net over F27, using
(19−5, 19, large)-Net in Base 27 — Upper bound on s
There is no (14, 19, large)-net in base 27, because
- 3 times m-reduction [i] would yield (14, 16, large)-net in base 27, but