Best Known (89−49, 89, s)-Nets in Base 16
(89−49, 89, 225)-Net over F16 — Constructive and digital
Digital (40, 89, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
(89−49, 89, 16984)-Net in Base 16 — Upper bound on s
There is no (40, 89, 16985)-net in base 16, because
- 1 times m-reduction [i] would yield (40, 88, 16985)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 9185 273495 178240 697660 605341 556214 536754 992590 186361 525637 969841 586838 127719 646376 606851 384022 759129 230101 > 1688 [i]