Best Known (9, 9+4, s)-Nets in Base 9
(9, 9+4, 6480)-Net over F9 — Constructive and digital
Digital (9, 13, 6480)-net over F9, using
- 1 times m-reduction [i] based on digital (9, 14, 6480)-net over F9, using
- net defined by OOA [i] based on linear OOA(914, 6480, F9, 5, 5) (dual of [(6480, 5), 32386, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(914, 12961, F9, 5) (dual of [12961, 12947, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), using
- trace code [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(914, 12961, F9, 5) (dual of [12961, 12947, 6]-code), using
- net defined by OOA [i] based on linear OOA(914, 6480, F9, 5, 5) (dual of [(6480, 5), 32386, 6]-NRT-code), using
(9, 9+4, 12962)-Net over F9 — Digital
Digital (9, 13, 12962)-net over F9, using
- net defined by OOA [i] based on linear OOA(913, 12962, F9, 4, 4) (dual of [(12962, 4), 51835, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(913, 12962, F9, 3, 4) (dual of [(12962, 3), 38873, 5]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(913, 12962, F9, 4) (dual of [12962, 12949, 5]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(912, 12960, F9, 4) (dual of [12960, 12948, 5]-code), using
- trace code [i] based on linear OA(816, 6480, F81, 4) (dual of [6480, 6474, 5]-code), using
- 1 times truncation [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- trace code [i] based on linear OA(816, 6480, F81, 4) (dual of [6480, 6474, 5]-code), using
- linear OA(912, 12961, F9, 3) (dual of [12961, 12949, 4]-code or 12961-cap in PG(11,9)), using Gilbert–Varšamov bound and bm = 912 > Vbs−1(k−1) = 5374 460161 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(912, 12960, F9, 4) (dual of [12960, 12948, 5]-code), using
- construction X with Varšamov bound [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(913, 12962, F9, 4) (dual of [12962, 12949, 5]-code), using
- appending kth column [i] based on linear OOA(913, 12962, F9, 3, 4) (dual of [(12962, 3), 38873, 5]-NRT-code), using
(9, 9+4, 281838)-Net in Base 9 — Upper bound on s
There is no (9, 13, 281839)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 2 541876 629745 > 913 [i]