Best Known (122−48, 122, s)-Nets in Base 5
(122−48, 122, 252)-Net over F5 — Constructive and digital
Digital (74, 122, 252)-net over F5, using
- 6 times m-reduction [i] based on digital (74, 128, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 64, 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, 64, 126)-net over F25, using
(122−48, 122, 285)-Net over F5 — Digital
Digital (74, 122, 285)-net over F5, using
(122−48, 122, 8740)-Net in Base 5 — Upper bound on s
There is no (74, 122, 8741)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 18 837912 932920 138776 177266 047978 491102 785562 676087 821946 532613 861389 671394 923851 544225 > 5122 [i]