Best Known (88−72, 88, s)-Nets in Base 25
(88−72, 88, 126)-Net over F25 — Constructive and digital
Digital (16, 88, 126)-net over F25, using
- t-expansion [i] based on digital (10, 88, 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
(88−72, 88, 150)-Net over F25 — Digital
Digital (16, 88, 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
(88−72, 88, 1535)-Net in Base 25 — Upper bound on s
There is no (16, 88, 1536)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 1044 333910 460320 215236 743902 690487 524937 413322 265949 942452 618791 377176 256370 224284 553862 909267 657936 418069 184808 571748 532225 > 2588 [i]