Best Known (85−15, 85, s)-Nets in Base 9
(85−15, 85, 75925)-Net over F9 — Constructive and digital
Digital (70, 85, 75925)-net over F9, using
- net defined by OOA [i] based on linear OOA(985, 75925, F9, 15, 15) (dual of [(75925, 15), 1138790, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(985, 531476, F9, 15) (dual of [531476, 531391, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(985, 531477, F9, 15) (dual of [531477, 531392, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(979, 531441, F9, 15) (dual of [531441, 531362, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(949, 531441, F9, 10) (dual of [531441, 531392, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(96, 36, F9, 4) (dual of [36, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(985, 531477, F9, 15) (dual of [531477, 531392, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(985, 531476, F9, 15) (dual of [531476, 531391, 16]-code), using
(85−15, 85, 531477)-Net over F9 — Digital
Digital (70, 85, 531477)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(985, 531477, F9, 15) (dual of [531477, 531392, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(979, 531441, F9, 15) (dual of [531441, 531362, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(949, 531441, F9, 10) (dual of [531441, 531392, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(96, 36, F9, 4) (dual of [36, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
(85−15, 85, large)-Net in Base 9 — Upper bound on s
There is no (70, 85, large)-net in base 9, because
- 13 times m-reduction [i] would yield (70, 72, large)-net in base 9, but