Best Known (9−4, 9, s)-Nets in Base 49
(9−4, 9, 3676)-Net over F49 — Constructive and digital
Digital (5, 9, 3676)-net over F49, using
- net defined by OOA [i] based on linear OOA(499, 3676, F49, 4, 4) (dual of [(3676, 4), 14695, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(499, 3676, F49, 3, 4) (dual of [(3676, 3), 11019, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(499, 7352, F49, 4) (dual of [7352, 7343, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(499, 7353, F49, 4) (dual of [7353, 7344, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(499, 7352, F49, 4) (dual of [7352, 7343, 5]-code), using
- appending kth column [i] based on linear OOA(499, 3676, F49, 3, 4) (dual of [(3676, 3), 11019, 5]-NRT-code), using
(9−4, 9, 7353)-Net over F49 — Digital
Digital (5, 9, 7353)-net over F49, using
- net defined by OOA [i] based on linear OOA(499, 7353, F49, 4, 4) (dual of [(7353, 4), 29403, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(499, 7353, F49, 3, 4) (dual of [(7353, 3), 22050, 5]-NRT-code), using
(9−4, 9, 1188929)-Net in Base 49 — Upper bound on s
There is no (5, 9, 1188930)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 1628 416319 509441 > 499 [i]