Best Known (124−44, 124, s)-Nets in Base 5
(124−44, 124, 252)-Net over F5 — Constructive and digital
Digital (80, 124, 252)-net over F5, using
- 16 times m-reduction [i] based on digital (80, 140, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 70, 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, 70, 126)-net over F25, using
(124−44, 124, 435)-Net over F5 — Digital
Digital (80, 124, 435)-net over F5, using
(124−44, 124, 19682)-Net in Base 5 — Upper bound on s
There is no (80, 124, 19683)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 470 243616 881109 283539 859507 377129 060339 452366 790246 100118 300656 639913 702369 764313 780905 > 5124 [i]