Best Known (78, 78+58, s)-Nets in Base 5
(78, 78+58, 252)-Net over F5 — Constructive and digital
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
(78, 78+58, 5512)-Net in Base 5 — Upper bound on s
There is no (78, 136, 5513)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 115302 554257 941580 542287 496755 914025 377748 581950 532835 084355 382920 526077 048523 474423 472826 692725 > 5136 [i]