Best Known (5, 55, s)-Nets in Base 49
(5, 55, 55)-Net over F49 — Constructive and digital
Digital (5, 55, 55)-net over F49, using
- net from sequence [i] based on digital (5, 54)-sequence over F49, using
(5, 55, 92)-Net over F49 — Digital
Digital (5, 55, 92)-net over F49, using
- t-expansion [i] based on digital (3, 55, 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
(5, 55, 1085)-Net in Base 49 — Upper bound on s
There is no (5, 55, 1086)-net in base 49, because
- 6 times m-reduction [i] would yield (5, 49, 1086)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 66149 255902 959409 163844 409537 412694 412044 685824 135728 144723 994502 775644 318438 522561 > 4949 [i]