Best Known (21, 21+29, s)-Nets in Base 3
(21, 21+29, 32)-Net over F3 — Constructive and digital
Digital (21, 50, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
(21, 21+29, 128)-Net in Base 3 — Upper bound on s
There is no (21, 50, 129)-net in base 3, because
- 1 times m-reduction [i] would yield (21, 49, 129)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 254387 380461 544008 943737 > 349 [i]