Best Known (78, 78+52, s)-Nets in Base 5
(78, 78+52, 252)-Net over F5 — Constructive and digital
Digital (78, 130, 252)-net over F5, using
- 6 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+52, 283)-Net over F5 — Digital
Digital (78, 130, 283)-net over F5, using
(78, 78+52, 8223)-Net in Base 5 — Upper bound on s
There is no (78, 130, 8224)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 7 347456 376262 443905 272159 360664 937801 233274 227746 687825 730265 719912 140538 706995 639163 806209 > 5130 [i]