Best Known (115−44, 115, s)-Nets in Base 5
(115−44, 115, 252)-Net over F5 — Constructive and digital
Digital (71, 115, 252)-net over F5, using
- 7 times m-reduction [i] based on 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
- trace code for nets [i] based on digital (10, 61, 126)-net over F25, using
(115−44, 115, 302)-Net over F5 — Digital
Digital (71, 115, 302)-net over F5, using
(115−44, 115, 10181)-Net in Base 5 — Upper bound on s
There is no (71, 115, 10182)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 240 921140 459408 395836 365645 616568 372439 547620 758219 955656 097908 664733 411526 076225 > 5115 [i]