Best Known (60, 60+12, s)-Nets in Base 9
(60, 60+12, 797164)-Net over F9 — Constructive and digital
Digital (60, 72, 797164)-net over F9, using
- net defined by OOA [i] based on linear OOA(972, 797164, F9, 12, 12) (dual of [(797164, 12), 9565896, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(972, 4782984, F9, 12) (dual of [4782984, 4782912, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(91, 15, F9, 1) (dual of [15, 14, 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
- OA 6-folding and stacking [i] based on linear OA(972, 4782984, F9, 12) (dual of [4782984, 4782912, 13]-code), using
(60, 60+12, 3372931)-Net over F9 — Digital
Digital (60, 72, 3372931)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(972, 3372931, F9, 12) (dual of [3372931, 3372859, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(972, 4782984, F9, 12) (dual of [4782984, 4782912, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(91, 15, F9, 1) (dual of [15, 14, 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(972, 4782984, F9, 12) (dual of [4782984, 4782912, 13]-code), using
(60, 60+12, large)-Net in Base 9 — Upper bound on s
There is no (60, 72, large)-net in base 9, because
- 10 times m-reduction [i] would yield (60, 62, large)-net in base 9, but