Best Known (69, 69+38, s)-Nets in Base 5
(69, 69+38, 252)-Net over F5 — Constructive and digital
Digital (69, 107, 252)-net over F5, using
- 11 times m-reduction [i] based on digital (69, 118, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 59, 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, 59, 126)-net over F25, using
(69, 69+38, 386)-Net over F5 — Digital
Digital (69, 107, 386)-net over F5, using
(69, 69+38, 17104)-Net in Base 5 — Upper bound on s
There is no (69, 107, 17105)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 616 612365 940690 597035 023339 156948 771309 758361 776141 911823 312562 675302 178685 > 5107 [i]