Best Known (163−54, 163, s)-Nets in Base 2
(163−54, 163, 68)-Net over F2 — Constructive and digital
Digital (109, 163, 68)-net over F2, using
- 13 times m-reduction [i] based on digital (109, 176, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 88, 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, 88, 34)-net over F4, using
(163−54, 163, 84)-Net in Base 2 — Constructive
(109, 163, 84)-net in base 2, using
- 1 times m-reduction [i] based on (109, 164, 84)-net in base 2, using
- trace code for nets [i] based on (27, 82, 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, 82, 42)-net in base 4, using
(163−54, 163, 119)-Net over F2 — Digital
Digital (109, 163, 119)-net over F2, using
(163−54, 163, 678)-Net in Base 2 — Upper bound on s
There is no (109, 163, 679)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 11 983353 190172 127165 773305 797136 919123 089230 156696 > 2163 [i]