Best Known (116−44, 116, s)-Nets in Base 5
(116−44, 116, 252)-Net over F5 — Constructive and digital
Digital (72, 116, 252)-net over F5, using
- 8 times m-reduction [i] based on digital (72, 124, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 62, 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, 62, 126)-net over F25, using
(116−44, 116, 315)-Net over F5 — Digital
Digital (72, 116, 315)-net over F5, using
(116−44, 116, 10955)-Net in Base 5 — Upper bound on s
There is no (72, 116, 10956)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1204 573964 112170 535946 627427 894349 785957 444552 447931 841997 603017 336009 460337 865025 > 5116 [i]