Best Known (163, 253, s)-Nets in Base 2
(163, 253, 112)-Net over F2 — Constructive and digital
Digital (163, 253, 112)-net over F2, using
- 7 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
(163, 253, 147)-Net over F2 — Digital
Digital (163, 253, 147)-net over F2, using
(163, 253, 803)-Net in Base 2 — Upper bound on s
There is no (163, 253, 804)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 14858 251615 572586 950615 942056 166891 845853 249836 555470 827517 297554 521182 302784 > 2253 [i]