Best Known (120−16, 120, s)-Nets in Base 9
(120−16, 120, 1048575)-Net over F9 — Constructive and digital
Digital (104, 120, 1048575)-net over F9, using
- 1 times m-reduction [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
(120−16, 120, large)-Net over F9 — Digital
Digital (104, 120, large)-net over F9, using
- 92 times duplication [i] based on digital (102, 118, large)-net over F9, using
- t-expansion [i] based on digital (101, 118, large)-net over F9, using
(120−16, 120, large)-Net in Base 9 — Upper bound on s
There is no (104, 120, large)-net in base 9, because
- 14 times m-reduction [i] would yield (104, 106, large)-net in base 9, but