Best Known (84, 84+42, s)-Nets in Base 9
(84, 84+42, 740)-Net over F9 — Constructive and digital
Digital (84, 126, 740)-net over F9, using
- 10 times m-reduction [i] based on digital (84, 136, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 68, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 68, 370)-net over F81, using
(84, 84+42, 1748)-Net over F9 — Digital
Digital (84, 126, 1748)-net over F9, using
(84, 84+42, 576564)-Net in Base 9 — Upper bound on s
There is no (84, 126, 576565)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 1 716166 012464 197257 927097 093086 136212 757322 408804 840021 733271 344542 009324 663100 201867 823025 817908 794297 476168 384693 872201 > 9126 [i]