Best Known (117−48, 117, s)-Nets in Base 5
(117−48, 117, 252)-Net over F5 — Constructive and digital
Digital (69, 117, 252)-net over F5, using
- 1 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
(117−48, 117, 6245)-Net in Base 5 — Upper bound on s
There is no (69, 117, 6246)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 6029 965725 872169 413239 685036 562527 841243 173128 845552 230734 609514 185122 540397 828225 > 5117 [i]