Best Known (45, 45+14, s)-Nets in Base 7
(45, 45+14, 1200)-Net over F7 — Constructive and digital
Digital (45, 59, 1200)-net over F7, using
- net defined by OOA [i] based on linear OOA(759, 1200, F7, 14, 14) (dual of [(1200, 14), 16741, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(759, 8400, F7, 14) (dual of [8400, 8341, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(759, 8402, F7, 14) (dual of [8402, 8343, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(759, 8400, F7, 14) (dual of [8400, 8341, 15]-code), using
(45, 45+14, 8402)-Net over F7 — Digital
Digital (45, 59, 8402)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(759, 8402, F7, 14) (dual of [8402, 8343, 15]-code), using
(45, 45+14, 7477154)-Net in Base 7 — Upper bound on s
There is no (45, 59, 7477155)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 72 574590 730478 164102 662711 480958 672210 183330 707127 > 759 [i]