Best Known (22, 22+29, s)-Nets in Base 49
(22, 22+29, 344)-Net over F49 — Constructive and digital
Digital (22, 51, 344)-net over F49, using
- t-expansion [i] based on digital (21, 51, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(22, 22+29, 136964)-Net in Base 49 — Upper bound on s
There is no (22, 51, 136965)-net in base 49, because
- 1 times m-reduction [i] would yield (22, 50, 136965)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 3 234483 056423 803735 947316 404696 158536 052899 407129 072874 606978 450285 772264 019250 424353 > 4950 [i]