Best Known (27, 31, s)-Nets in Base 8
(27, 31, large)-Net over F8 — Constructive and digital
Digital (27, 31, large)-net over F8, using
- 83 times duplication [i] based on digital (24, 28, large)-net over F8, using
- net defined by OOA [i] based on linear OOA(828, large, F8, 4, 4), using
- appending kth column [i] based on linear OOA(828, large, F8, 3, 4), using
- (u, u+v)-construction [i] based on
- linear OOA(82, 9, F8, 3, 2) (dual of [(9, 3), 25, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;25,8) [i]
- linear OOA(826, 8388602, F8, 3, 4) (dual of [(8388602, 3), 25165780, 5]-NRT-code), using
- trace code [i] based on linear OOA(6413, 4194301, F64, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(6413, 8388602, F64, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6413, large, F64, 4) (dual of [large, large−13, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(6413, large, F64, 4) (dual of [large, large−13, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(6413, 8388602, F64, 4) (dual of [8388602, 8388589, 5]-code), using
- trace code [i] based on linear OOA(6413, 4194301, F64, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
- linear OOA(82, 9, F8, 3, 2) (dual of [(9, 3), 25, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(828, large, F8, 3, 4), using
- net defined by OOA [i] based on linear OOA(828, large, F8, 4, 4), using
(27, 31, large)-Net in Base 8 — Upper bound on s
There is no (27, 31, large)-net in base 8, because
- 2 times m-reduction [i] would yield (27, 29, large)-net in base 8, but