Best Known (173−58, 173, s)-Nets in Base 2
(173−58, 173, 68)-Net over F2 — Constructive and digital
Digital (115, 173, 68)-net over F2, using
- 15 times m-reduction [i] based on digital (115, 188, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 94, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second 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) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- trace code for nets [i] based on digital (21, 94, 34)-net over F4, using
(173−58, 173, 84)-Net in Base 2 — Constructive
(115, 173, 84)-net in base 2, using
- 3 times m-reduction [i] based on (115, 176, 84)-net in base 2, using
- trace code for nets [i] based on (27, 88, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- trace code for nets [i] based on (27, 88, 42)-net in base 4, using
(173−58, 173, 122)-Net over F2 — Digital
Digital (115, 173, 122)-net over F2, using
(173−58, 173, 687)-Net in Base 2 — Upper bound on s
There is no (115, 173, 688)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 12238 442848 236406 245689 051442 286581 984548 509908 693246 > 2173 [i]