Best Known (78−67, 78, s)-Nets in Base 25
(78−67, 78, 126)-Net over F25 — Constructive and digital
Digital (11, 78, 126)-net over F25, using
- t-expansion [i] based on digital (10, 78, 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
(78−67, 78, 985)-Net in Base 25 — Upper bound on s
There is no (11, 78, 986)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 77, 986)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 452486 171694 782842 874500 271601 940035 679748 079483 601951 833688 069869 186637 948080 137569 585471 945199 530008 069745 > 2577 [i]