Best Known (72, 108, s)-Nets in Base 5
(72, 108, 252)-Net over F5 — Constructive and digital
Digital (72, 108, 252)-net over F5, using
- 16 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
(72, 108, 515)-Net over F5 — Digital
Digital (72, 108, 515)-net over F5, using
(72, 108, 29491)-Net in Base 5 — Upper bound on s
There is no (72, 108, 29492)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 3082 190057 098700 300790 968871 941118 684182 057199 600431 788850 683743 907105 420225 > 5108 [i]