Best Known (1, 1+41, s)-Nets in Base 49
(1, 1+41, 51)-Net over F49 — Constructive and digital
Digital (1, 42, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
(1, 1+41, 64)-Net over F49 — Digital
Digital (1, 42, 64)-net over F49, using
- net from sequence [i] based on digital (1, 63)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 1 and N(F) ≥ 64, using
(1, 1+41, 281)-Net in Base 49 — Upper bound on s
There is no (1, 42, 282)-net in base 49, because
- 31 times m-reduction [i] would yield (1, 11, 282)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 3 929889 617545 981537 > 4911 [i]