Best Known (76−58, 76, s)-Nets in Base 25
(76−58, 76, 126)-Net over F25 — Constructive and digital
Digital (18, 76, 126)-net over F25, using
- t-expansion [i] based on digital (10, 76, 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
(76−58, 76, 153)-Net over F25 — Digital
Digital (18, 76, 153)-net over F25, using
- net from sequence [i] based on digital (18, 152)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 18 and N(F) ≥ 153, using
(76−58, 76, 2226)-Net in Base 25 — Upper bound on s
There is no (18, 76, 2227)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 17744 283261 424175 109192 050853 521702 655262 381251 340125 513488 120445 888057 950223 369030 250820 305331 392141 837225 > 2576 [i]