Best Known (121, 121+66, s)-Nets in Base 2
(121, 121+66, 68)-Net over F2 — Constructive and digital
Digital (121, 187, 68)-net over F2, using
- 13 times m-reduction [i] based on digital (121, 200, 68)-net over F2, using
- trace code for nets [i] based on digital (21, 100, 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, 100, 34)-net over F4, using
(121, 121+66, 84)-Net in Base 2 — Constructive
(121, 187, 84)-net in base 2, using
- 1 times m-reduction [i] based on (121, 188, 84)-net in base 2, using
- trace code for nets [i] based on (27, 94, 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, 94, 42)-net in base 4, using
(121, 121+66, 116)-Net over F2 — Digital
Digital (121, 187, 116)-net over F2, using
(121, 121+66, 621)-Net in Base 2 — Upper bound on s
There is no (121, 187, 622)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 203 907055 239347 004889 625328 789601 630113 528372 010526 362405 > 2187 [i]