Best Known (8, 53, s)-Nets in Base 49
(8, 53, 58)-Net over F49 — Constructive and digital
Digital (8, 53, 58)-net over F49, using
- net from sequence [i] based on digital (8, 57)-sequence over F49, using
(8, 53, 92)-Net over F49 — Digital
Digital (8, 53, 92)-net over F49, using
- t-expansion [i] based on digital (3, 53, 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
(8, 53, 1853)-Net in Base 49 — Upper bound on s
There is no (8, 53, 1854)-net in base 49, because
- 1 times m-reduction [i] would yield (8, 52, 1854)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 7783 820841 340891 489718 342402 372380 903133 191379 228023 263539 243573 513986 938749 027844 153025 > 4952 [i]