Best Known (32−10, 32, s)-Nets in Base 7
(32−10, 32, 240)-Net over F7 — Constructive and digital
Digital (22, 32, 240)-net over F7, using
- net defined by OOA [i] based on linear OOA(732, 240, F7, 10, 10) (dual of [(240, 10), 2368, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(732, 1200, F7, 10) (dual of [1200, 1168, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(732, 1201, F7, 10) (dual of [1201, 1169, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(732, 1200, F7, 10) (dual of [1200, 1168, 11]-code), using
(32−10, 32, 1177)-Net over F7 — Digital
Digital (22, 32, 1177)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(732, 1177, F7, 10) (dual of [1177, 1145, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(732, 1201, F7, 10) (dual of [1201, 1169, 11]-code), using
(32−10, 32, 111250)-Net in Base 7 — Upper bound on s
There is no (22, 32, 111251)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 1104 459829 259265 616121 745307 > 732 [i]