Best Known (73−58, 73, s)-Nets in Base 25
(73−58, 73, 126)-Net over F25 — Constructive and digital
Digital (15, 73, 126)-net over F25, using
- t-expansion [i] based on digital (10, 73, 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
(73−58, 73, 140)-Net over F25 — Digital
Digital (15, 73, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(73−58, 73, 1591)-Net in Base 25 — Upper bound on s
There is no (15, 73, 1592)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 1 136120 044166 410087 989418 736246 526095 962809 108210 342317 935535 061845 241509 298324 466906 434433 832928 166465 > 2573 [i]