Best Known (74, 74+39, s)-Nets in Base 5
(74, 74+39, 252)-Net over F5 — Constructive and digital
Digital (74, 113, 252)-net over F5, using
- 15 times m-reduction [i] based on digital (74, 128, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 64, 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, 64, 126)-net over F25, using
(74, 74+39, 455)-Net over F5 — Digital
Digital (74, 113, 455)-net over F5, using
(74, 74+39, 26131)-Net in Base 5 — Upper bound on s
There is no (74, 113, 26132)-net in base 5, because
- 1 times m-reduction [i] would yield (74, 112, 26132)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1 926040 293868 727611 099149 247047 179741 672315 048171 358366 163644 255352 481109 452625 > 5112 [i]