Best Known (11, 11+8, s)-Nets in Base 7
(11, 11+8, 102)-Net over F7 — Constructive and digital
Digital (11, 19, 102)-net over F7, using
- 1 times m-reduction [i] based on digital (11, 20, 102)-net over F7, using
- trace code for nets [i] based on digital (1, 10, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- trace code for nets [i] based on digital (1, 10, 51)-net over F49, using
(11, 11+8, 171)-Net over F7 — Digital
Digital (11, 19, 171)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(719, 171, F7, 2, 8) (dual of [(171, 2), 323, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(719, 342, F7, 8) (dual of [342, 323, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 2-folding [i] based on linear OA(719, 342, F7, 8) (dual of [342, 323, 9]-code), using
(11, 11+8, 3809)-Net in Base 7 — Upper bound on s
There is no (11, 19, 3810)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 11404 626429 020041 > 719 [i]