Best Known (4, 4+41, s)-Nets in Base 49
(4, 4+41, 54)-Net over F49 — Constructive and digital
Digital (4, 45, 54)-net over F49, using
- net from sequence [i] based on digital (4, 53)-sequence over F49, using
(4, 4+41, 92)-Net over F49 — Digital
Digital (4, 45, 92)-net over F49, using
- t-expansion [i] based on digital (3, 45, 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, 4+41, 888)-Net in Base 49 — Upper bound on s
There is no (4, 45, 889)-net in base 49, because
- 5 times m-reduction [i] would yield (4, 40, 889)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 41 088966 398763 740281 328466 068448 579671 833172 781869 603508 312578 911585 > 4940 [i]