Best Known (128−48, 128, s)-Nets in Base 4
(128−48, 128, 130)-Net over F4 — Constructive and digital
Digital (80, 128, 130)-net over F4, using
- 20 times m-reduction [i] based on digital (80, 148, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 74, 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, 74, 65)-net over F16, using
(128−48, 128, 249)-Net over F4 — Digital
Digital (80, 128, 249)-net over F4, using
(128−48, 128, 5292)-Net in Base 4 — Upper bound on s
There is no (80, 128, 5293)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 116231 817554 945512 585233 607433 951959 460204 597905 234616 679264 381386 960167 891534 > 4128 [i]