Best Known (64−25, 64, s)-Nets in Base 7
(64−25, 64, 114)-Net over F7 — Constructive and digital
Digital (39, 64, 114)-net over F7, using
- trace code for nets [i] based on digital (7, 32, 57)-net over F49, using
- net from sequence [i] based on digital (7, 56)-sequence over F49, using
(64−25, 64, 312)-Net over F7 — Digital
Digital (39, 64, 312)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(764, 312, F7, 25) (dual of [312, 248, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(764, 342, F7, 25) (dual of [342, 278, 26]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(764, 342, F7, 25) (dual of [342, 278, 26]-code), using
(64−25, 64, 24090)-Net in Base 7 — Upper bound on s
There is no (39, 64, 24091)-net in base 7, because
- 1 times m-reduction [i] would yield (39, 63, 24091)-net in base 7, but
- the generalized Rao bound for nets shows that 7m ≥ 174324 329469 730946 630933 407257 058657 709142 054582 161881 > 763 [i]