Best Known (31−9, 31, s)-Nets in Base 9
(31−9, 31, 819)-Net over F9 — Constructive and digital
Digital (22, 31, 819)-net over F9, using
- net defined by OOA [i] based on linear OOA(931, 819, F9, 9, 9) (dual of [(819, 9), 7340, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(931, 3277, F9, 9) (dual of [3277, 3246, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(931, 3280, F9, 9) (dual of [3280, 3249, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(931, 3277, F9, 9) (dual of [3277, 3246, 10]-code), using
(31−9, 31, 3280)-Net over F9 — Digital
Digital (22, 31, 3280)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(931, 3280, F9, 9) (dual of [3280, 3249, 10]-code), using
(31−9, 31, 3969916)-Net in Base 9 — Upper bound on s
There is no (22, 31, 3969917)-net in base 9, because
- 1 times m-reduction [i] would yield (22, 30, 3969917)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 42391 158869 314655 344988 343329 > 930 [i]