Best Known (96−17, 96, s)-Nets in Base 9
(96−17, 96, 66433)-Net over F9 — Constructive and digital
Digital (79, 96, 66433)-net over F9, using
- 91 times duplication [i] based on digital (78, 95, 66433)-net over F9, using
- net defined by OOA [i] based on linear OOA(995, 66433, F9, 17, 17) (dual of [(66433, 17), 1129266, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(995, 531465, F9, 17) (dual of [531465, 531370, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(995, 531469, F9, 17) (dual of [531469, 531374, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(991, 531441, F9, 17) (dual of [531441, 531350, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(967, 531441, F9, 13) (dual of [531441, 531374, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(94, 28, F9, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,9)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(995, 531469, F9, 17) (dual of [531469, 531374, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(995, 531465, F9, 17) (dual of [531465, 531370, 18]-code), using
- net defined by OOA [i] based on linear OOA(995, 66433, F9, 17, 17) (dual of [(66433, 17), 1129266, 18]-NRT-code), using
(96−17, 96, 531471)-Net over F9 — Digital
Digital (79, 96, 531471)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(996, 531471, F9, 17) (dual of [531471, 531375, 18]-code), using
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(11) [i] based on
- linear OA(991, 531441, F9, 17) (dual of [531441, 531350, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(967, 531441, F9, 13) (dual of [531441, 531374, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(961, 531441, F9, 12) (dual of [531441, 531380, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(94, 29, F9, 3) (dual of [29, 25, 4]-code or 29-cap in PG(3,9)), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(16) ⊂ Ce(12) ⊂ Ce(11) [i] based on
(96−17, 96, large)-Net in Base 9 — Upper bound on s
There is no (79, 96, large)-net in base 9, because
- 15 times m-reduction [i] would yield (79, 81, large)-net in base 9, but