Best Known (62−12, 62, s)-Nets in Base 9
(62−12, 62, 88575)-Net over F9 — Constructive and digital
Digital (50, 62, 88575)-net over F9, using
- net defined by OOA [i] based on linear OOA(962, 88575, F9, 12, 12) (dual of [(88575, 12), 1062838, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(962, 531450, F9, 12) (dual of [531450, 531388, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(962, 531454, F9, 12) (dual of [531454, 531392, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- 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(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(91, 13, F9, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(962, 531454, F9, 12) (dual of [531454, 531392, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(962, 531450, F9, 12) (dual of [531450, 531388, 13]-code), using
(62−12, 62, 374765)-Net over F9 — Digital
Digital (50, 62, 374765)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(962, 374765, F9, 12) (dual of [374765, 374703, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(962, 531454, F9, 12) (dual of [531454, 531392, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- 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(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(91, 13, F9, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(962, 531454, F9, 12) (dual of [531454, 531392, 13]-code), using
(62−12, 62, large)-Net in Base 9 — Upper bound on s
There is no (50, 62, large)-net in base 9, because
- 10 times m-reduction [i] would yield (50, 52, large)-net in base 9, but