Best Known (83−25, 83, s)-Nets in Base 9
(83−25, 83, 740)-Net over F9 — Constructive and digital
Digital (58, 83, 740)-net over F9, using
- 1 times m-reduction [i] based on digital (58, 84, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 42, 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, 42, 370)-net over F81, using
(83−25, 83, 2457)-Net over F9 — Digital
Digital (58, 83, 2457)-net over F9, using
(83−25, 83, 2192437)-Net in Base 9 — Upper bound on s
There is no (58, 83, 2192438)-net in base 9, because
- 1 times m-reduction [i] would yield (58, 82, 2192438)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1 769649 951764 857088 668950 016263 623962 993303 038663 876668 105066 008106 752975 694529 > 982 [i]