Best Known (175, 256, s)-Nets in Base 2
(175, 256, 112)-Net over F2 — Constructive and digital
Digital (175, 256, 112)-net over F2, using
- t-expansion [i] based on digital (163, 256, 112)-net over F2, using
- 4 times m-reduction [i] based on digital (163, 260, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 130, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- trace code for nets [i] based on digital (33, 130, 56)-net over F4, using
- 4 times m-reduction [i] based on digital (163, 260, 112)-net over F2, using
(175, 256, 195)-Net over F2 — Digital
Digital (175, 256, 195)-net over F2, using
(175, 256, 1250)-Net in Base 2 — Upper bound on s
There is no (175, 256, 1251)-net in base 2, because
- 1 times m-reduction [i] would yield (175, 255, 1251)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 58856 982926 937913 007143 871315 656639 855291 383297 133360 810624 442533 598312 557176 > 2255 [i]