Best Known (52−45, 52, s)-Nets in Base 49
(52−45, 52, 57)-Net over F49 — Constructive and digital
Digital (7, 52, 57)-net over F49, using
- net from sequence [i] based on digital (7, 56)-sequence over F49, using
(52−45, 52, 92)-Net over F49 — Digital
Digital (7, 52, 92)-net over F49, using
- t-expansion [i] based on digital (3, 52, 92)-net over F49, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
- net from sequence [i] based on digital (3, 91)-sequence over F49, using
(52−45, 52, 1551)-Net in Base 49 — Upper bound on s
There is no (7, 52, 1552)-net in base 49, because
- 1 times m-reduction [i] would yield (7, 51, 1552)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 159 692894 720079 734458 980252 643829 190691 724573 975400 786974 584702 837292 560876 624802 118145 > 4951 [i]