Best Known (62−49, 62, s)-Nets in Base 25
(62−49, 62, 126)-Net over F25 — Constructive and digital
Digital (13, 62, 126)-net over F25, using
- t-expansion [i] based on digital (10, 62, 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
(62−49, 62, 1447)-Net in Base 25 — Upper bound on s
There is no (13, 62, 1448)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 61, 1448)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 19 064538 975557 706987 160053 175805 751500 137097 410779 264221 939012 641605 649860 561162 100225 > 2561 [i]