Best Known (3, 3+41, s)-Nets in Base 49
(3, 3+41, 53)-Net over F49 — Constructive and digital
Digital (3, 44, 53)-net over F49, using
- net from sequence [i] based on digital (3, 52)-sequence over F49, using
(3, 3+41, 92)-Net over F49 — Digital
Digital (3, 44, 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
(3, 3+41, 689)-Net in Base 49 — Upper bound on s
There is no (3, 44, 690)-net in base 49, because
- 13 times m-reduction [i] would yield (3, 31, 690)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 25135 318834 925955 294352 218974 734045 280807 471579 583553 > 4931 [i]