Best Known (142−55, 142, s)-Nets in Base 5
(142−55, 142, 252)-Net over F5 — Constructive and digital
Digital (87, 142, 252)-net over F5, using
- t-expansion [i] based on digital (85, 142, 252)-net over F5, using
- 8 times m-reduction [i] based on digital (85, 150, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 75, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 75, 126)-net over F25, using
- 8 times m-reduction [i] based on digital (85, 150, 252)-net over F5, using
(142−55, 142, 343)-Net over F5 — Digital
Digital (87, 142, 343)-net over F5, using
(142−55, 142, 12184)-Net in Base 5 — Upper bound on s
There is no (87, 142, 12185)-net in base 5, because
- 1 times m-reduction [i] would yield (87, 141, 12185)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 358 844201 192849 979355 957158 294413 029985 011433 788913 161997 978778 598453 743512 270937 458063 243233 105533 > 5141 [i]