Best Known (78, 78+50, s)-Nets in Base 5
(78, 78+50, 252)-Net over F5 — Constructive and digital
Digital (78, 128, 252)-net over F5, using
- 8 times m-reduction [i] based on digital (78, 136, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 68, 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, 68, 126)-net over F25, using
(78, 78+50, 305)-Net over F5 — Digital
Digital (78, 128, 305)-net over F5, using
(78, 78+50, 9626)-Net in Base 5 — Upper bound on s
There is no (78, 128, 9627)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 294223 503208 910112 250899 209714 821151 491763 882009 543954 856668 620976 239930 608969 657718 244365 > 5128 [i]