Best Known (17, 17+11, s)-Nets in Base 3
(17, 17+11, 56)-Net over F3 — Constructive and digital
Digital (17, 28, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 14, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
(17, 17+11, 486)-Net in Base 3 — Upper bound on s
There is no (17, 28, 487)-net in base 3, because
- 1 times m-reduction [i] would yield (17, 27, 487)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 7 647336 600327 > 327 [i]