Best Known (116, 116+60, s)-Nets in Base 2
(116, 116+60, 68)-Net over F2 — Constructive and digital
Digital (116, 176, 68)-net over F2, using
- 14 times m-reduction [i] based on digital (116, 190, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 95, 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, 95, 34)-net over F4, using
(116, 116+60, 84)-Net in Base 2 — Constructive
(116, 176, 84)-net in base 2, using
- 2 times m-reduction [i] based on (116, 178, 84)-net in base 2, using
- trace code for nets [i] based on (27, 89, 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, 89, 42)-net in base 4, using
(116, 116+60, 119)-Net over F2 — Digital
Digital (116, 176, 119)-net over F2, using
(116, 116+60, 659)-Net in Base 2 — Upper bound on s
There is no (116, 176, 660)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 97665 841609 849788 692277 866086 787548 396172 004810 660064 > 2176 [i]