Best Known (4, 4+31, s)-Nets in Base 49
(4, 4+31, 54)-Net over F49 — Constructive and digital
Digital (4, 35, 54)-net over F49, using
- net from sequence [i] based on digital (4, 53)-sequence over F49, using
(4, 4+31, 92)-Net over F49 — Digital
Digital (4, 35, 92)-net over F49, using
- t-expansion [i] based on digital (3, 35, 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+31, 899)-Net in Base 49 — Upper bound on s
There is no (4, 35, 900)-net in base 49, because
- 1 times m-reduction [i] would yield (4, 34, 900)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 2940 227383 481176 849111 556701 670645 193656 546081 376825 625921 > 4934 [i]