Best Known (122−58, 122, s)-Nets in Base 3
(122−58, 122, 56)-Net over F3 — Constructive and digital
Digital (64, 122, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 61, 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
(122−58, 122, 76)-Net over F3 — Digital
Digital (64, 122, 76)-net over F3, using
(122−58, 122, 565)-Net in Base 3 — Upper bound on s
There is no (64, 122, 566)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 16669 963110 763192 136546 788829 737133 961592 188311 849283 835797 > 3122 [i]