Best Known (104−91, 104, s)-Nets in Base 25
(104−91, 104, 126)-Net over F25 — Constructive and digital
Digital (13, 104, 126)-net over F25, using
- t-expansion [i] based on digital (10, 104, 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
(104−91, 104, 1139)-Net in Base 25 — Upper bound on s
There is no (13, 104, 1140)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 103, 1140)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 990034 981911 382772 980668 430233 982869 486751 455923 906431 764055 573860 165234 395287 042741 628925 148698 973229 355070 982225 344464 356390 594980 843673 161825 > 25103 [i]