Best Known (40, 40+69, s)-Nets in Base 16
(40, 40+69, 225)-Net over F16 — Constructive and digital
Digital (40, 109, 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
(40, 40+69, 6010)-Net in Base 16 — Upper bound on s
There is no (40, 109, 6011)-net in base 16, because
- 1 times m-reduction [i] would yield (40, 108, 6011)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 11146 017338 164211 483804 221262 204101 924936 786604 034869 290389 270958 660778 589682 420663 201658 995370 643990 227574 719267 990519 242595 649961 > 16108 [i]