Best Known (110−44, 110, s)-Nets in Base 5
(110−44, 110, 252)-Net over F5 — Constructive and digital
Digital (66, 110, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (66, 112, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 56, 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, 56, 126)-net over F25, using
(110−44, 110, 7057)-Net in Base 5 — Upper bound on s
There is no (66, 110, 7058)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 77119 966345 722318 582130 315508 403884 782077 753603 497854 869816 771282 027364 104705 > 5110 [i]