Best Known (76−63, 76, s)-Nets in Base 25
(76−63, 76, 126)-Net over F25 — Constructive and digital
Digital (13, 76, 126)-net over F25, using
- t-expansion [i] based on digital (10, 76, 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
(76−63, 76, 1230)-Net in Base 25 — Upper bound on s
There is no (13, 76, 1231)-net in base 25, because
- 1 times m-reduction [i] would yield (13, 75, 1231)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 701 481105 941088 277148 413090 729107 812308 108935 781732 446748 887993 170870 927548 327568 118388 223094 881307 926425 > 2575 [i]