Best Known (71, 122, s)-Nets in Base 5
(71, 122, 252)-Net over F5 — Constructive and digital
Digital (71, 122, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 61, 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
(71, 122, 6127)-Net in Base 5 — Upper bound on s
There is no (71, 122, 6128)-net in base 5, because
- 1 times m-reduction [i] would yield (71, 121, 6128)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 3 767690 927851 855713 568131 515731 561777 826524 395140 136199 039682 391348 656456 980805 741505 > 5121 [i]