Best Known (102, 102+72, s)-Nets in Base 4
(102, 102+72, 130)-Net over F4 — Constructive and digital
Digital (102, 174, 130)-net over F4, using
- 18 times m-reduction [i] based on digital (102, 192, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 96, 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, 96, 65)-net over F16, using
(102, 102+72, 232)-Net over F4 — Digital
Digital (102, 174, 232)-net over F4, using
(102, 102+72, 3839)-Net in Base 4 — Upper bound on s
There is no (102, 174, 3840)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 576 842629 726969 682852 651556 002875 594236 862346 731577 568274 891385 544096 108015 762804 272991 279831 263026 177369 > 4174 [i]