Best Known (128, 166, s)-Nets in Base 8
(128, 166, 1724)-Net over F8 — Constructive and digital
Digital (128, 166, 1724)-net over F8, using
- net defined by OOA [i] based on linear OOA(8166, 1724, F8, 38, 38) (dual of [(1724, 38), 65346, 39]-NRT-code), using
- OA 19-folding and stacking [i] based on linear OA(8166, 32756, F8, 38) (dual of [32756, 32590, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using
- an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- discarding factors / shortening the dual code based on linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using
- OA 19-folding and stacking [i] based on linear OA(8166, 32756, F8, 38) (dual of [32756, 32590, 39]-code), using
(128, 166, 28084)-Net over F8 — Digital
Digital (128, 166, 28084)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8166, 28084, F8, 38) (dual of [28084, 27918, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using
- an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- discarding factors / shortening the dual code based on linear OA(8166, 32768, F8, 38) (dual of [32768, 32602, 39]-code), using
(128, 166, large)-Net in Base 8 — Upper bound on s
There is no (128, 166, large)-net in base 8, because
- 36 times m-reduction [i] would yield (128, 130, large)-net in base 8, but