Best Known (55−28, 55, s)-Nets in Base 9
(55−28, 55, 82)-Net over F9 — Constructive and digital
Digital (27, 55, 82)-net over F9, using
- base reduction for projective spaces (embedding PG(27,81) in PG(54,9)) for nets [i] based on digital (0, 28, 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
(55−28, 55, 84)-Net in Base 9 — Constructive
(27, 55, 84)-net in base 9, using
- 2 times m-reduction [i] based on (27, 57, 84)-net in base 9, using
- base change [i] based on digital (8, 38, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- base change [i] based on digital (8, 38, 84)-net over F27, using
(55−28, 55, 116)-Net over F9 — Digital
Digital (27, 55, 116)-net over F9, using
(55−28, 55, 4229)-Net in Base 9 — Upper bound on s
There is no (27, 55, 4230)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 30440 822225 899865 865280 242383 447887 658959 719684 450401 > 955 [i]