Best Known (127−20, 127, s)-Nets in Base 9
(127−20, 127, 478301)-Net over F9 — Constructive and digital
Digital (107, 127, 478301)-net over F9, using
- net defined by OOA [i] based on linear OOA(9127, 478301, F9, 20, 20) (dual of [(478301, 20), 9565893, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(9127, 4783010, F9, 20) (dual of [4783010, 4782883, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(9127, 4783011, F9, 20) (dual of [4783011, 4782884, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(9120, 4782969, F9, 20) (dual of [4782969, 4782849, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(97, 42, F9, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(9127, 4783011, F9, 20) (dual of [4783011, 4782884, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(9127, 4783010, F9, 20) (dual of [4783010, 4782883, 21]-code), using
(127−20, 127, 4515820)-Net over F9 — Digital
Digital (107, 127, 4515820)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9127, 4515820, F9, 20) (dual of [4515820, 4515693, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(9127, 4783011, F9, 20) (dual of [4783011, 4782884, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(9120, 4782969, F9, 20) (dual of [4782969, 4782849, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(97, 42, F9, 5) (dual of [42, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(9127, 4783011, F9, 20) (dual of [4783011, 4782884, 21]-code), using
(127−20, 127, large)-Net in Base 9 — Upper bound on s
There is no (107, 127, large)-net in base 9, because
- 18 times m-reduction [i] would yield (107, 109, large)-net in base 9, but