Best Known (16, 23, s)-Nets in Base 81
(16, 23, 183709)-Net over F81 — Constructive and digital
Digital (16, 23, 183709)-net over F81, using
- net defined by OOA [i] based on linear OOA(8123, 183709, F81, 9, 7) (dual of [(183709, 9), 1653358, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(8123, 183710, F81, 3, 7) (dual of [(183710, 3), 551107, 8]-NRT-code), using
- (u, u+v)-construction [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
- 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(814, 6562, F81, 3, 3) (dual of [(6562, 3), 19682, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(8123, 183710, F81, 3, 7) (dual of [(183710, 3), 551107, 8]-NRT-code), using
(16, 23, 774449)-Net over F81 — Digital
Digital (16, 23, 774449)-net over F81, using
(16, 23, large)-Net in Base 81 — Upper bound on s
There is no (16, 23, large)-net in base 81, because
- 5 times m-reduction [i] would yield (16, 18, large)-net in base 81, but