Best Known (55−30, 55, s)-Nets in Base 128
(55−30, 55, 438)-Net over F128 — Constructive and digital
Digital (25, 55, 438)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (9, 39, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- digital (1, 16, 150)-net over F128, using
(55−30, 55, 517)-Net in Base 128 — Constructive
(25, 55, 517)-net in base 128, using
- 1 times m-reduction [i] based on (25, 56, 517)-net in base 128, using
- base change [i] based on digital (18, 49, 517)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (2, 33, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- digital (1, 16, 258)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (18, 49, 517)-net over F256, using
(55−30, 55, 926)-Net over F128 — Digital
Digital (25, 55, 926)-net over F128, using
(55−30, 55, 2694004)-Net in Base 128 — Upper bound on s
There is no (25, 55, 2694005)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 78 804202 259237 062958 036826 286886 346623 569388 497827 465692 481687 434838 622236 310211 919452 153119 419557 503631 302494 799312 > 12855 [i]