Best Known (10, 10+55, s)-Nets in Base 25
(10, 10+55, 126)-Net over F25 — Constructive and digital
Digital (10, 65, 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
(10, 10+55, 923)-Net in Base 25 — Upper bound on s
There is no (10, 65, 924)-net in base 25, because
- 1 times m-reduction [i] would yield (10, 64, 924)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 301407 906968 979044 686467 244378 711998 287778 874848 397924 019937 371312 352890 465563 634786 392417 > 2564 [i]