Best Known (55−43, 55, s)-Nets in Base 25
(55−43, 55, 126)-Net over F25 — Constructive and digital
Digital (12, 55, 126)-net over F25, using
- t-expansion [i] based on digital (10, 55, 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
(55−43, 55, 1411)-Net in Base 25 — Upper bound on s
There is no (12, 55, 1412)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 54, 1412)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 3107 924346 758296 037500 256537 715847 373851 981576 545216 184941 371584 392717 783265 > 2554 [i]