Best Known (24, 24+16, s)-Nets in Base 7
(24, 24+16, 108)-Net over F7 — Constructive and digital
Digital (24, 40, 108)-net over F7, using
- trace code for nets [i] based on digital (4, 20, 54)-net over F49, using
- net from sequence [i] based on digital (4, 53)-sequence over F49, using
(24, 24+16, 220)-Net over F7 — Digital
Digital (24, 40, 220)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(740, 220, F7, 16) (dual of [220, 180, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(740, 342, F7, 16) (dual of [342, 302, 17]-code), using
(24, 24+16, 10539)-Net in Base 7 — Upper bound on s
There is no (24, 40, 10540)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 6368 057651 899291 036276 529785 846849 > 740 [i]