Best Known (78−62, 78, s)-Nets in Base 25
(78−62, 78, 126)-Net over F25 — Constructive and digital
Digital (16, 78, 126)-net over F25, using
- t-expansion [i] based on digital (10, 78, 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
(78−62, 78, 150)-Net over F25 — Digital
Digital (16, 78, 150)-net over F25, using
- net from sequence [i] based on digital (16, 149)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 16 and N(F) ≥ 150, using
(78−62, 78, 1686)-Net in Base 25 — Upper bound on s
There is no (16, 78, 1687)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 10 995315 092782 944692 799779 804752 545456 473071 227097 630191 154861 028457 109751 033979 373824 895196 345554 110879 370201 > 2578 [i]