Best Known (42−18, 42, s)-Nets in Base 3
(42−18, 42, 56)-Net over F3 — Constructive and digital
Digital (24, 42, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 21, 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
(42−18, 42, 340)-Net in Base 3 — Upper bound on s
There is no (24, 42, 341)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 109 539785 294380 670219 > 342 [i]