Best Known (4, 33, s)-Nets in Base 49
(4, 33, 54)-Net over F49 — Constructive and digital
Digital (4, 33, 54)-net over F49, using
- net from sequence [i] based on digital (4, 53)-sequence over F49, using
(4, 33, 92)-Net over F49 — Digital
Digital (4, 33, 92)-net over F49, using
- t-expansion [i] based on digital (3, 33, 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
(4, 33, 912)-Net in Base 49 — Upper bound on s
There is no (4, 33, 913)-net in base 49, because
- 1 times m-reduction [i] would yield (4, 32, 913)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 1 226166 138907 306201 737795 554174 217134 457402 426459 936673 > 4932 [i]