Best Known (52, 52+46, s)-Nets in Base 3
(52, 52+46, 56)-Net over F3 — Constructive and digital
Digital (52, 98, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 49, 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
(52, 52+46, 66)-Net over F3 — Digital
Digital (52, 98, 66)-net over F3, using
(52, 52+46, 486)-Net in Base 3 — Upper bound on s
There is no (52, 98, 487)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 58552 725068 438012 657153 118030 472681 758626 474739 > 398 [i]