Best Known (52−43, 52, s)-Nets in Base 49
(52−43, 52, 59)-Net over F49 — Constructive and digital
Digital (9, 52, 59)-net over F49, using
- net from sequence [i] based on digital (9, 58)-sequence over F49, using
(52−43, 52, 92)-Net over F49 — Digital
Digital (9, 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
(52−43, 52, 2291)-Net in Base 49 — Upper bound on s
There is no (9, 52, 2292)-net in base 49, because
- 1 times m-reduction [i] would yield (9, 51, 2292)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 159 818747 115944 945562 230780 616690 482517 454190 782496 044971 875522 470714 222851 115532 682433 > 4951 [i]