Best Known (69, 69+42, s)-Nets in Base 5
(69, 69+42, 252)-Net over F5 — Constructive and digital
Digital (69, 111, 252)-net over F5, using
- 7 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+42, 307)-Net over F5 — Digital
Digital (69, 111, 307)-net over F5, using
(69, 69+42, 10724)-Net in Base 5 — Upper bound on s
There is no (69, 111, 10725)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 385666 106809 018326 859051 105562 694318 700339 884417 931223 379350 510121 951110 336901 > 5111 [i]