Best Known (15−4, 15, s)-Nets in Base 27
(15−4, 15, 265750)-Net over F27 — Constructive and digital
Digital (11, 15, 265750)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 28)-net over F27, using
- digital (9, 13, 265722)-net over F27, using
- net defined by OOA [i] based on linear OOA(2713, 265722, F27, 4, 4) (dual of [(265722, 4), 1062875, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2713, 531444, F27, 4) (dual of [531444, 531431, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- 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, 531441, F27, 3) (dual of [531441, 531432, 4]-code or 531441-cap in PG(8,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(2713, 531444, F27, 4) (dual of [531444, 531431, 5]-code), using
- net defined by OOA [i] based on linear OOA(2713, 265722, F27, 4, 4) (dual of [(265722, 4), 1062875, 5]-NRT-code), using
(15−4, 15, 1002836)-Net over F27 — Digital
Digital (11, 15, 1002836)-net over F27, using
(15−4, 15, large)-Net in Base 27 — Upper bound on s
There is no (11, 15, large)-net in base 27, because
- 2 times m-reduction [i] would yield (11, 13, large)-net in base 27, but