Best Known (128−18, 128, s)-Nets in Base 9
(128−18, 128, 932067)-Net over F9 — Constructive and digital
Digital (110, 128, 932067)-net over F9, using
- net defined by OOA [i] based on linear OOA(9128, 932067, F9, 18, 18) (dual of [(932067, 18), 16777078, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9128, large, F9, 18) (dual of [large, large−128, 19]-code), using
- the narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(9128, large, F9, 18) (dual of [large, large−128, 19]-code), using
(128−18, 128, large)-Net over F9 — Digital
Digital (110, 128, large)-net over F9, using
- 1 times m-reduction [i] based on digital (110, 129, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9129, large, F9, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 916−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(9129, large, F9, 19) (dual of [large, large−129, 20]-code), using
(128−18, 128, large)-Net in Base 9 — Upper bound on s
There is no (110, 128, large)-net in base 9, because
- 16 times m-reduction [i] would yield (110, 112, large)-net in base 9, but