Best Known (110, 110+17, s)-Nets in Base 9
(110, 110+17, 1048575)-Net over F9 — Constructive and digital
Digital (110, 127, 1048575)-net over F9, using
- 96 times duplication [i] based on digital (104, 121, 1048575)-net over F9, using
- net defined by OOA [i] based on linear OOA(9121, 1048575, F9, 17, 17) (dual of [(1048575, 17), 17825654, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9121, 8388601, F9, 17) (dual of [8388601, 8388480, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9121, large, F9, 17) (dual of [large, large−121, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(9121, large, F9, 17) (dual of [large, large−121, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9121, 8388601, F9, 17) (dual of [8388601, 8388480, 18]-code), using
- net defined by OOA [i] based on linear OOA(9121, 1048575, F9, 17, 17) (dual of [(1048575, 17), 17825654, 18]-NRT-code), using
(110, 110+17, large)-Net over F9 — Digital
Digital (110, 127, large)-net over F9, using
- 2 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
(110, 110+17, large)-Net in Base 9 — Upper bound on s
There is no (110, 127, large)-net in base 9, because
- 15 times m-reduction [i] would yield (110, 112, large)-net in base 9, but