Best Known (20−6, 20, s)-Nets in Base 81
(20−6, 20, 183710)-Net over F81 — Constructive and digital
Digital (14, 20, 183710)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 6562)-net over F81, using
- net defined by OOA [i] based on linear OOA(814, 6562, F81, 3, 3) (dual of [(6562, 3), 19682, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(814, 6562, F81, 2, 3) (dual of [(6562, 2), 13120, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(814, 6562, F81, 3, 3) (dual of [(6562, 3), 19682, 4]-NRT-code), using
- digital (10, 16, 177148)-net over F81, using
- net defined by OOA [i] based on linear OOA(8116, 177148, F81, 6, 6) (dual of [(177148, 6), 1062872, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- OA 3-folding and stacking [i] based on linear OA(8116, 531444, F81, 6) (dual of [531444, 531428, 7]-code), using
- net defined by OOA [i] based on linear OOA(8116, 177148, F81, 6, 6) (dual of [(177148, 6), 1062872, 7]-NRT-code), using
- digital (1, 4, 6562)-net over F81, using
(20−6, 20, 1401803)-Net over F81 — Digital
Digital (14, 20, 1401803)-net over F81, using
(20−6, 20, large)-Net in Base 81 — Upper bound on s
There is no (14, 20, large)-net in base 81, because
- 4 times m-reduction [i] would yield (14, 16, large)-net in base 81, but