Best Known (35, 35+34, s)-Nets in Base 7
(35, 35+34, 100)-Net over F7 — Constructive and digital
Digital (35, 69, 100)-net over F7, using
- 1 times m-reduction [i] based on digital (35, 70, 100)-net over F7, using
- trace code for nets [i] based on digital (0, 35, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- trace code for nets [i] based on digital (0, 35, 50)-net over F49, using
(35, 35+34, 120)-Net over F7 — Digital
Digital (35, 69, 120)-net over F7, using
(35, 35+34, 3209)-Net in Base 7 — Upper bound on s
There is no (35, 69, 3210)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 20555 862627 180785 539929 728093 565022 503954 937039 826652 413725 > 769 [i]