Best Known (15−4, 15, s)-Nets in Base 7
(15−4, 15, 4201)-Net over F7 — Constructive and digital
Digital (11, 15, 4201)-net over F7, using
- net defined by OOA [i] based on linear OOA(715, 4201, F7, 4, 4) (dual of [(4201, 4), 16789, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(715, 4201, F7, 3, 4) (dual of [(4201, 3), 12588, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(715, 8402, F7, 4) (dual of [8402, 8387, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(715, 8403, F7, 4) (dual of [8403, 8388, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(715, 8402, F7, 4) (dual of [8402, 8387, 5]-code), using
- appending kth column [i] based on linear OOA(715, 4201, F7, 3, 4) (dual of [(4201, 3), 12588, 5]-NRT-code), using
(15−4, 15, 8403)-Net over F7 — Digital
Digital (11, 15, 8403)-net over F7, using
- net defined by OOA [i] based on linear OOA(715, 8403, F7, 4, 4) (dual of [(8403, 4), 33597, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(715, 8403, F7, 3, 4) (dual of [(8403, 3), 25194, 5]-NRT-code), using
(15−4, 15, 513568)-Net in Base 7 — Upper bound on s
There is no (11, 15, 513569)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 4 747571 526769 > 715 [i]