Best Known (42−27, 42, s)-Nets in Base 25
(42−27, 42, 126)-Net over F25 — Constructive and digital
Digital (15, 42, 126)-net over F25, using
- t-expansion [i] based on digital (10, 42, 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
(42−27, 42, 140)-Net over F25 — Digital
Digital (15, 42, 140)-net over F25, using
- net from sequence [i] based on digital (15, 139)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 15 and N(F) ≥ 140, using
(42−27, 42, 6048)-Net in Base 25 — Upper bound on s
There is no (15, 42, 6049)-net in base 25, because
- 1 times m-reduction [i] would yield (15, 41, 6049)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 2072 302662 290155 615233 720508 523121 727135 594335 638893 823929 > 2541 [i]