Best Known (144, 144+90, s)-Nets in Base 2
(144, 144+90, 76)-Net over F2 — Constructive and digital
Digital (144, 234, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (45, 90, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- digital (54, 144, 42)-net over F2, using
- net from sequence [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
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- digital (45, 90, 34)-net over F2, using
(144, 144+90, 84)-Net in Base 2 — Constructive
(144, 234, 84)-net in base 2, using
- trace code for nets [i] based on (27, 117, 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
(144, 144+90, 115)-Net over F2 — Digital
Digital (144, 234, 115)-net over F2, using
(144, 144+90, 583)-Net in Base 2 — Upper bound on s
There is no (144, 234, 584)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 27733 136429 497560 878811 955898 222020 256422 568044 869352 441701 058001 146120 > 2234 [i]