Best Known (15, 15+80, s)-Nets in Base 25
(15, 15+80, 126)-Net over F25 — Constructive and digital
Digital (15, 95, 126)-net over F25, using
- t-expansion [i] based on digital (10, 95, 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
(15, 15+80, 140)-Net over F25 — Digital
Digital (15, 95, 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
(15, 15+80, 1351)-Net in Base 25 — Upper bound on s
There is no (15, 95, 1352)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 6 379872 383243 793066 562686 919720 203591 645061 839206 744558 642896 450001 987029 578765 651751 018088 215774 665566 011613 457413 635996 080388 422145 > 2595 [i]