Best Known (79, 79+44, s)-Nets in Base 5
(79, 79+44, 252)-Net over F5 — Constructive and digital
Digital (79, 123, 252)-net over F5, using
- 15 times m-reduction [i] based on digital (79, 138, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 69, 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, 69, 126)-net over F25, using
(79, 79+44, 418)-Net over F5 — Digital
Digital (79, 123, 418)-net over F5, using
(79, 79+44, 18293)-Net in Base 5 — Upper bound on s
There is no (79, 123, 18294)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 94 122653 379191 649077 338933 660521 606750 317180 250894 691762 416678 841458 945321 453677 931585 > 5123 [i]