Best Known (9, 9+4, s)-Nets in Base 16
(9, 9+4, 65280)-Net over F16 — Constructive and digital
Digital (9, 13, 65280)-net over F16, using
- 1 times m-reduction [i] based on digital (9, 14, 65280)-net over F16, using
- net defined by OOA [i] based on linear OOA(1614, 65280, F16, 5, 5) (dual of [(65280, 5), 326386, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(1614, 130561, F16, 5) (dual of [130561, 130547, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- trace code [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(1614, 130561, F16, 5) (dual of [130561, 130547, 6]-code), using
- net defined by OOA [i] based on linear OOA(1614, 65280, F16, 5, 5) (dual of [(65280, 5), 326386, 6]-NRT-code), using
(9, 9+4, 130562)-Net over F16 — Digital
Digital (9, 13, 130562)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1613, 130562, F16, 4) (dual of [130562, 130549, 5]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(1612, 130560, F16, 4) (dual of [130560, 130548, 5]-code), using
- trace code [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- 1 times truncation [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- trace code [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- linear OA(1612, 130561, F16, 3) (dual of [130561, 130549, 4]-code or 130561-cap in PG(11,16)), using Gilbert–Varšamov bound and bm = 1612 > Vbs−1(k−1) = 1 917652 550401 [i]
- linear OA(160, 1, F16, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(1612, 130560, F16, 4) (dual of [130560, 130548, 5]-code), using
- construction X with Varšamov bound [i] based on
(9, 9+4, 6327083)-Net in Base 16 — Upper bound on s
There is no (9, 13, 6327084)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 4503 599995 203271 > 1613 [i]