Best Known (51−37, 51, s)-Nets in Base 49
(51−37, 51, 64)-Net over F49 — Constructive and digital
Digital (14, 51, 64)-net over F49, using
- net from sequence [i] based on digital (14, 63)-sequence over F49, using
(51−37, 51, 92)-Net over F49 — Digital
Digital (14, 51, 92)-net over F49, using
- t-expansion [i] based on digital (3, 51, 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
(51−37, 51, 7787)-Net in Base 49 — Upper bound on s
There is no (14, 51, 7788)-net in base 49, because
- 1 times m-reduction [i] would yield (14, 50, 7788)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 3 240181 911687 294011 812701 958133 463832 626219 401660 540601 592752 371159 086823 212605 631105 > 4950 [i]