Best Known (49−41, 49, s)-Nets in Base 27
(49−41, 49, 84)-Net over F27 — Constructive and digital
Digital (8, 49, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
(49−41, 49, 92)-Net over F27 — Digital
Digital (8, 49, 92)-net over F27, using
- net from sequence [i] based on digital (8, 91)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 92, using
(49−41, 49, 859)-Net in Base 27 — Upper bound on s
There is no (8, 49, 860)-net in base 27, because
- 1 times m-reduction [i] would yield (8, 48, 860)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 508 320764 290742 140942 213910 187527 982590 720243 640252 292872 060326 989953 > 2748 [i]