Best Known (89−22, 89, s)-Nets in Base 7
(89−22, 89, 688)-Net over F7 — Constructive and digital
Digital (67, 89, 688)-net over F7, using
- 3 times m-reduction [i] based on digital (67, 92, 688)-net over F7, using
- trace code for nets [i] based on digital (21, 46, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- trace code for nets [i] based on digital (21, 46, 344)-net over F49, using
(89−22, 89, 5530)-Net over F7 — Digital
Digital (67, 89, 5530)-net over F7, using
(89−22, 89, 5629551)-Net in Base 7 — Upper bound on s
There is no (67, 89, 5629552)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 1635 784243 263281 337506 026291 878532 902737 324808 401390 827010 636959 403432 192257 > 789 [i]