Best Known (16, 16+52, s)-Nets in Base 25
(16, 16+52, 126)-Net over F25 — Constructive and digital
Digital (16, 68, 126)-net over F25, using
- t-expansion [i] based on digital (10, 68, 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
(16, 16+52, 150)-Net over F25 — Digital
Digital (16, 68, 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
(16, 16+52, 1978)-Net in Base 25 — Upper bound on s
There is no (16, 68, 1979)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 116033 169247 820891 926307 251924 823388 382822 925911 446981 268958 915117 084314 347887 126809 809579 053137 > 2568 [i]