Best Known (37−29, 37, s)-Nets in Base 49
(37−29, 37, 58)-Net over F49 — Constructive and digital
Digital (8, 37, 58)-net over F49, using
- net from sequence [i] based on digital (8, 57)-sequence over F49, using
(37−29, 37, 92)-Net over F49 — Digital
Digital (8, 37, 92)-net over F49, using
- t-expansion [i] based on digital (3, 37, 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
(37−29, 37, 2788)-Net in Base 49 — Upper bound on s
There is no (8, 37, 2789)-net in base 49, because
- 1 times m-reduction [i] would yield (8, 36, 2789)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 7 047392 058767 493190 628270 081201 450725 751550 523039 014306 563617 > 4936 [i]