Best Known (42, 42+36, s)-Nets in Base 7
(42, 42+36, 106)-Net over F7 — Constructive and digital
Digital (42, 78, 106)-net over F7, using
- trace code for nets [i] based on digital (3, 39, 53)-net over F49, using
- net from sequence [i] based on digital (3, 52)-sequence over F49, using
(42, 42+36, 184)-Net over F7 — Digital
Digital (42, 78, 184)-net over F7, using
- trace code for nets [i] based on digital (3, 39, 92)-net over F49, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
(42, 42+36, 5770)-Net in Base 7 — Upper bound on s
There is no (42, 78, 5771)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 828806 101242 691514 217542 348074 585703 298989 296723 693673 771435 340013 > 778 [i]