Best Known (70, 117, s)-Nets in Base 9
(70, 117, 344)-Net over F9 — Constructive and digital
Digital (70, 117, 344)-net over F9, using
- 9 times m-reduction [i] based on digital (70, 126, 344)-net over F9, using
- trace code for nets [i] based on digital (7, 63, 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, 63, 172)-net over F81, using
(70, 117, 612)-Net over F9 — Digital
Digital (70, 117, 612)-net over F9, using
(70, 117, 76557)-Net in Base 9 — Upper bound on s
There is no (70, 117, 76558)-net in base 9, because
- 1 times m-reduction [i] would yield (70, 116, 76558)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 492 230650 944185 132686 727445 736586 685735 726541 749261 158349 669067 737405 146285 815574 619424 676562 514416 946280 964945 > 9116 [i]