Best Known (17, 17+7, s)-Nets in Base 81
(17, 17+7, 193465)-Net over F81 — Constructive and digital
Digital (17, 24, 193465)-net over F81, using
- net defined by OOA [i] based on linear OOA(8124, 193465, F81, 9, 7) (dual of [(193465, 9), 1741161, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(8124, 193466, F81, 3, 7) (dual of [(193466, 3), 580374, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(815, 16318, F81, 3, 3) (dual of [(16318, 3), 48949, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(815, 16318, F81, 2, 3) (dual of [(16318, 2), 32631, 4]-NRT-code), using
- linear OOA(8119, 177148, F81, 3, 7) (dual of [(177148, 3), 531425, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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(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(6) ⊂ Ce(5) [i] based on
- OOA 3-folding [i] based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- linear OOA(815, 16318, F81, 3, 3) (dual of [(16318, 3), 48949, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(8124, 193466, F81, 3, 7) (dual of [(193466, 3), 580374, 8]-NRT-code), using
(17, 17+7, 1610916)-Net over F81 — Digital
Digital (17, 24, 1610916)-net over F81, using
(17, 17+7, large)-Net in Base 81 — Upper bound on s
There is no (17, 24, large)-net in base 81, because
- 5 times m-reduction [i] would yield (17, 19, large)-net in base 81, but