Best Known (21, 43, s)-Nets in Base 9
(21, 43, 82)-Net over F9 — Constructive and digital
Digital (21, 43, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(21,81) in PG(42,9)) for nets [i] based on digital (0, 22, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(21, 43, 97)-Net over F9 — Digital
Digital (21, 43, 97)-net over F9, using
(21, 43, 3290)-Net in Base 9 — Upper bound on s
There is no (21, 43, 3291)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 107815 275562 914281 183117 913157 553024 134345 > 943 [i]