Best Known (64−49, 64, s)-Nets in Base 25
(64−49, 64, 126)-Net over F25 — Constructive and digital
Digital (15, 64, 126)-net over F25, using
- t-expansion [i] based on digital (10, 64, 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
(64−49, 64, 140)-Net over F25 — Digital
Digital (15, 64, 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
(64−49, 64, 1896)-Net in Base 25 — Upper bound on s
There is no (15, 64, 1897)-net in base 25, because
- 1 times m-reduction [i] would yield (15, 63, 1897)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 11866 795122 813485 956113 494990 996588 544296 974125 045805 461822 870378 199254 363332 806498 530625 > 2563 [i]