Best Known (107−17, 107, s)-Nets in Base 9
(107−17, 107, 597872)-Net over F9 — Constructive and digital
Digital (90, 107, 597872)-net over F9, using
- net defined by OOA [i] based on linear OOA(9107, 597872, F9, 17, 17) (dual of [(597872, 17), 10163717, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9107, 4782977, F9, 17) (dual of [4782977, 4782870, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9107, 4782984, F9, 17) (dual of [4782984, 4782877, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(9107, 4782984, F9, 17) (dual of [4782984, 4782877, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9107, 4782977, F9, 17) (dual of [4782977, 4782870, 18]-code), using
(107−17, 107, 4446206)-Net over F9 — Digital
Digital (90, 107, 4446206)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9107, 4446206, F9, 17) (dual of [4446206, 4446099, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9107, 4782984, F9, 17) (dual of [4782984, 4782877, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(9107, 4782984, F9, 17) (dual of [4782984, 4782877, 18]-code), using
(107−17, 107, large)-Net in Base 9 — Upper bound on s
There is no (90, 107, large)-net in base 9, because
- 15 times m-reduction [i] would yield (90, 92, large)-net in base 9, but