Best Known (11, 11+33, s)-Nets in Base 25
(11, 11+33, 126)-Net over F25 — Constructive and digital
Digital (11, 44, 126)-net over F25, using
- t-expansion [i] based on digital (10, 44, 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
(11, 11+33, 1611)-Net in Base 25 — Upper bound on s
There is no (11, 44, 1612)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 43, 1612)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 305189 244152 589226 262704 621961 712092 193356 848640 957744 920065 > 2543 [i]