Best Known (105−42, 105, s)-Nets in Base 9
(105−42, 105, 344)-Net over F9 — Constructive and digital
Digital (63, 105, 344)-net over F9, using
- 7 times m-reduction [i] based on digital (63, 112, 344)-net over F9, using
- trace code for nets [i] based on digital (7, 56, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 56, 172)-net over F81, using
(105−42, 105, 576)-Net over F9 — Digital
Digital (63, 105, 576)-net over F9, using
(105−42, 105, 64051)-Net in Base 9 — Upper bound on s
There is no (63, 105, 64052)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 15686 634027 409153 134711 120088 785887 875028 938481 734016 930205 636072 633654 125105 827009 125770 098273 438497 > 9105 [i]