Best Known (108, 108+24, s)-Nets in Base 9
(108, 108+24, 44289)-Net over F9 — Constructive and digital
Digital (108, 132, 44289)-net over F9, using
- 91 times duplication [i] based on digital (107, 131, 44289)-net over F9, using
- net defined by OOA [i] based on linear OOA(9131, 44289, F9, 24, 24) (dual of [(44289, 24), 1062805, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9131, 531468, F9, 24) (dual of [531468, 531337, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9131, 531469, F9, 24) (dual of [531469, 531338, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(19) [i] based on
- linear OA(9127, 531441, F9, 24) (dual of [531441, 531314, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(9103, 531441, F9, 20) (dual of [531441, 531338, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(23) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(9131, 531469, F9, 24) (dual of [531469, 531338, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9131, 531468, F9, 24) (dual of [531468, 531337, 25]-code), using
- net defined by OOA [i] based on linear OOA(9131, 44289, F9, 24, 24) (dual of [(44289, 24), 1062805, 25]-NRT-code), using
(108, 108+24, 531471)-Net over F9 — Digital
Digital (108, 132, 531471)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9132, 531471, F9, 24) (dual of [531471, 531339, 25]-code), using
- construction XX applied to Ce(23) ⊂ Ce(19) ⊂ Ce(18) [i] based on
- linear OA(9127, 531441, F9, 24) (dual of [531441, 531314, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(9103, 531441, F9, 20) (dual of [531441, 531338, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(23) ⊂ Ce(19) ⊂ Ce(18) [i] based on
(108, 108+24, large)-Net in Base 9 — Upper bound on s
There is no (108, 132, large)-net in base 9, because
- 22 times m-reduction [i] would yield (108, 110, large)-net in base 9, but