Best Known (72, 72+42, s)-Nets in Base 5
(72, 72+42, 252)-Net over F5 — Constructive and digital
Digital (72, 114, 252)-net over F5, using
- 10 times m-reduction [i] based on digital (72, 124, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 62, 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, 62, 126)-net over F25, using
(72, 72+42, 349)-Net over F5 — Digital
Digital (72, 114, 349)-net over F5, using
(72, 72+42, 13500)-Net in Base 5 — Upper bound on s
There is no (72, 114, 13501)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 48 182824 302824 695070 516821 747824 865736 765776 177658 871125 126097 050885 761577 553125 > 5114 [i]