Best Known (164, 164+81, s)-Nets in Base 2
(164, 164+81, 112)-Net over F2 — Constructive and digital
Digital (164, 245, 112)-net over F2, using
- t-expansion [i] based on digital (163, 245, 112)-net over F2, using
- 15 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
- 15 times m-reduction [i] based on digital (163, 260, 112)-net over F2, using
(164, 164+81, 169)-Net over F2 — Digital
Digital (164, 245, 169)-net over F2, using
(164, 164+81, 1023)-Net in Base 2 — Upper bound on s
There is no (164, 245, 1024)-net in base 2, because
- 1 times m-reduction [i] would yield (164, 244, 1024)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 28 718545 727065 589779 972705 656640 214580 436378 874627 814966 924271 768889 055777 > 2244 [i]