Best Known (72−61, 72, s)-Nets in Base 25
(72−61, 72, 126)-Net over F25 — Constructive and digital
Digital (11, 72, 126)-net over F25, using
- t-expansion [i] based on digital (10, 72, 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
(72−61, 72, 1005)-Net in Base 25 — Upper bound on s
There is no (11, 72, 1006)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 71, 1006)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1829 429605 984081 739372 496401 639308 486860 368725 655456 323321 344073 335894 049181 783821 484794 595745 874465 > 2571 [i]