Best Known (47, 47+29, s)-Nets in Base 7
(47, 47+29, 118)-Net over F7 — Constructive and digital
Digital (47, 76, 118)-net over F7, using
- trace code for nets [i] based on digital (9, 38, 59)-net over F49, using
- net from sequence [i] based on digital (9, 58)-sequence over F49, using
(47, 47+29, 385)-Net over F7 — Digital
Digital (47, 76, 385)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(776, 385, F7, 29) (dual of [385, 309, 30]-code), using
- 38 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 12 times 0, 1, 20 times 0) [i] based on linear OA(773, 344, F7, 29) (dual of [344, 271, 30]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 344 | 76−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- 38 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 12 times 0, 1, 20 times 0) [i] based on linear OA(773, 344, F7, 29) (dual of [344, 271, 30]-code), using
(47, 47+29, 33923)-Net in Base 7 — Upper bound on s
There is no (47, 76, 33924)-net in base 7, because
- 1 times m-reduction [i] would yield (47, 75, 33924)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 2412 074697 748534 297699 425603 821815 295626 907313 811675 321492 145017 > 775 [i]