Best Known (34, 34+22, s)-Nets in Base 4
(34, 34+22, 130)-Net over F4 — Constructive and digital
Digital (34, 56, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 28, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(34, 34+22, 1892)-Net in Base 4 — Upper bound on s
There is no (34, 56, 1893)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 5219 364240 837452 128330 948527 344080 > 456 [i]