Best Known (60−15, 60, s)-Nets in Base 7
(60−15, 60, 1200)-Net over F7 — Constructive and digital
Digital (45, 60, 1200)-net over F7, using
- net defined by OOA [i] based on linear OOA(760, 1200, F7, 15, 15) (dual of [(1200, 15), 17940, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(760, 8401, F7, 15) (dual of [8401, 8341, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(760, 8403, F7, 15) (dual of [8403, 8343, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(760, 8401, F7, 15) (dual of [8401, 8341, 16]-code), using
(60−15, 60, 6459)-Net over F7 — Digital
Digital (45, 60, 6459)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(760, 6459, F7, 15) (dual of [6459, 6399, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(760, 8403, F7, 15) (dual of [8403, 8343, 16]-code), using
(60−15, 60, 7477154)-Net in Base 7 — Upper bound on s
There is no (45, 60, 7477155)-net in base 7, because
- 1 times m-reduction [i] would yield (45, 59, 7477155)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 72 574590 730478 164102 662711 480958 672210 183330 707127 > 759 [i]