Best Known (69−34, 69, s)-Nets in Base 16
(69−34, 69, 514)-Net over F16 — Constructive and digital
Digital (35, 69, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (35, 70, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 35, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 35, 257)-net over F256, using
(69−34, 69, 36902)-Net in Base 16 — Upper bound on s
There is no (35, 69, 36903)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 121439 019533 065923 060743 034596 105165 297720 018536 133950 581984 563672 629740 613763 015116 > 1669 [i]