Best Known (109−48, 109, s)-Nets in Base 4
(109−48, 109, 130)-Net over F4 — Constructive and digital
Digital (61, 109, 130)-net over F4, using
- 1 times m-reduction [i] based on digital (61, 110, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 55, 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
- trace code for nets [i] based on digital (6, 55, 65)-net over F16, using
(109−48, 109, 1753)-Net in Base 4 — Upper bound on s
There is no (61, 109, 1754)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 426255 422394 246727 480343 871753 761434 262862 418169 404657 348593 011029 > 4109 [i]