Best Known (105−36, 105, s)-Nets in Base 5
(105−36, 105, 252)-Net over F5 — Constructive and digital
Digital (69, 105, 252)-net over F5, using
- 13 times m-reduction [i] based on digital (69, 118, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 59, 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, 59, 126)-net over F25, using
(105−36, 105, 444)-Net over F5 — Digital
Digital (69, 105, 444)-net over F5, using
(105−36, 105, 22549)-Net in Base 5 — Upper bound on s
There is no (69, 105, 22550)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 24 653640 807505 498914 924935 310595 093760 857532 630757 284622 028190 466042 618241 > 5105 [i]