Best Known (89−31, 89, s)-Nets in Base 9
(89−31, 89, 448)-Net over F9 — Constructive and digital
Digital (58, 89, 448)-net over F9, using
- 1 times m-reduction [i] based on digital (58, 90, 448)-net over F9, using
- trace code for nets [i] based on digital (13, 45, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- trace code for nets [i] based on digital (13, 45, 224)-net over F81, using
(89−31, 89, 1035)-Net over F9 — Digital
Digital (58, 89, 1035)-net over F9, using
(89−31, 89, 318337)-Net in Base 9 — Upper bound on s
There is no (58, 89, 318338)-net in base 9, because
- 1 times m-reduction [i] would yield (58, 88, 318338)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 940500 558550 029378 681128 694161 903767 807681 442945 070671 045429 299960 520832 849569 557425 > 988 [i]