Best Known (7, 7+101, s)-Nets in Base 27
(7, 7+101, 82)-Net over F27 — Constructive and digital
Digital (7, 108, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
(7, 7+101, 705)-Net in Base 27 — Upper bound on s
There is no (7, 108, 706)-net in base 27, because
- 47 times m-reduction [i] would yield (7, 61, 706)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2064 914177 408427 292506 270002 896480 465906 475390 478888 579383 784534 978326 164990 732740 268945 > 2761 [i]