Best Known (60, 74, s)-Nets in Base 9
(60, 74, 75922)-Net over F9 — Constructive and digital
Digital (60, 74, 75922)-net over F9, using
- net defined by OOA [i] based on linear OOA(974, 75922, F9, 14, 14) (dual of [(75922, 14), 1062834, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(974, 531454, F9, 14) (dual of [531454, 531380, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(973, 531441, F9, 14) (dual of [531441, 531368, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(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(13) ⊂ Ce(11) [i] based on
- OA 7-folding and stacking [i] based on linear OA(974, 531454, F9, 14) (dual of [531454, 531380, 15]-code), using
(60, 74, 421930)-Net over F9 — Digital
Digital (60, 74, 421930)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(974, 421930, F9, 14) (dual of [421930, 421856, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(974, 531454, F9, 14) (dual of [531454, 531380, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(973, 531441, F9, 14) (dual of [531441, 531368, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(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(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(974, 531454, F9, 14) (dual of [531454, 531380, 15]-code), using
(60, 74, large)-Net in Base 9 — Upper bound on s
There is no (60, 74, large)-net in base 9, because
- 12 times m-reduction [i] would yield (60, 62, large)-net in base 9, but