Best Known (82, 82+56, s)-Nets in Base 4
(82, 82+56, 130)-Net over F4 — Constructive and digital
Digital (82, 138, 130)-net over F4, using
- 14 times m-reduction [i] based on digital (82, 152, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 76, 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, 76, 65)-net over F16, using
(82, 82+56, 203)-Net over F4 — Digital
Digital (82, 138, 203)-net over F4, using
(82, 82+56, 3470)-Net in Base 4 — Upper bound on s
There is no (82, 138, 3471)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 122325 298603 872020 716490 620566 333964 680831 005105 934254 649608 626687 456283 703139 862632 > 4138 [i]