Best Known (96, 114, s)-Nets in Base 9
(96, 114, 531442)-Net over F9 — Constructive and digital
Digital (96, 114, 531442)-net over F9, using
- net defined by OOA [i] based on linear OOA(9114, 531442, F9, 18, 18) (dual of [(531442, 18), 9565842, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9114, 4782978, F9, 18) (dual of [4782978, 4782864, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9114, 4782984, F9, 18) (dual of [4782984, 4782870, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(9114, 4782984, F9, 18) (dual of [4782984, 4782870, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(9114, 4782978, F9, 18) (dual of [4782978, 4782864, 19]-code), using
(96, 114, 4664291)-Net over F9 — Digital
Digital (96, 114, 4664291)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9114, 4664291, F9, 18) (dual of [4664291, 4664177, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9114, 4782984, F9, 18) (dual of [4782984, 4782870, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(18) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(9114, 4782984, F9, 18) (dual of [4782984, 4782870, 19]-code), using
(96, 114, large)-Net in Base 9 — Upper bound on s
There is no (96, 114, large)-net in base 9, because
- 16 times m-reduction [i] would yield (96, 98, large)-net in base 9, but