Best Known (73−61, 73, s)-Nets in Base 25
(73−61, 73, 126)-Net over F25 — Constructive and digital
Digital (12, 73, 126)-net over F25, using
- t-expansion [i] based on digital (10, 73, 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
(73−61, 73, 1120)-Net in Base 25 — Upper bound on s
There is no (12, 73, 1121)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 72, 1121)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 44880 703403 212570 349189 908521 532822 526588 529736 275509 139652 759352 679935 726308 541602 108961 953977 198481 > 2572 [i]