Best Known (24, 24+43, s)-Nets in Base 256
(24, 24+43, 517)-Net over F256 — Constructive and digital
Digital (24, 67, 517)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 22, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (2, 45, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (1, 22, 258)-net over F256, using
(24, 24+43, 1025)-Net over F256 — Digital
Digital (24, 67, 1025)-net over F256, using
- net from sequence [i] based on digital (24, 1024)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
- K1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 24 and N(F) ≥ 1025, using
(24, 24+43, 1260965)-Net in Base 256 — Upper bound on s
There is no (24, 67, 1260966)-net in base 256, because
- 1 times m-reduction [i] would yield (24, 66, 1260966)-net in base 256, but
- the generalized Rao bound for nets shows that 256m ≥ 878 706237 741133 034122 406723 460628 718704 857925 807694 006376 383003 536226 724298 447836 443880 191411 954133 678521 343127 511172 490074 995782 965671 569133 062983 750648 331306 > 25666 [i]