Best Known (13, 13+93, s)-Nets in Base 25
(13, 13+93, 126)-Net over F25 — Constructive and digital
Digital (13, 106, 126)-net over F25, using
- t-expansion [i] based on digital (10, 106, 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
(13, 13+93, 1139)-Net in Base 25 — Upper bound on s
There is no (13, 106, 1140)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 105, 1140)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 614 020209 951601 302516 032181 948232 003194 345415 655080 138994 483444 220836 822600 271887 201370 295172 789244 738572 394246 261193 701548 856344 616973 292625 253825 > 25105 [i]