Best Known (87, 87+23, s)-Nets in Base 9
(87, 87+23, 5371)-Net over F9 — Constructive and digital
Digital (87, 110, 5371)-net over F9, using
- 91 times duplication [i] based on digital (86, 109, 5371)-net over F9, using
- net defined by OOA [i] based on linear OOA(9109, 5371, F9, 23, 23) (dual of [(5371, 23), 123424, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9109, 59082, F9, 23) (dual of [59082, 58973, 24]-code), using
- 1 times code embedding in larger space [i] based on linear OA(9108, 59081, F9, 23) (dual of [59081, 58973, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(97, 32, F9, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(9108, 59081, F9, 23) (dual of [59081, 58973, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9109, 59082, F9, 23) (dual of [59082, 58973, 24]-code), using
- net defined by OOA [i] based on linear OOA(9109, 5371, F9, 23, 23) (dual of [(5371, 23), 123424, 24]-NRT-code), using
(87, 87+23, 66842)-Net over F9 — Digital
Digital (87, 110, 66842)-net over F9, using
(87, 87+23, large)-Net in Base 9 — Upper bound on s
There is no (87, 110, large)-net in base 9, because
- 21 times m-reduction [i] would yield (87, 89, large)-net in base 9, but