Best Known (136, 136+76, s)-Nets in Base 2
(136, 136+76, 76)-Net over F2 — Constructive and digital
Digital (136, 212, 76)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 77, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- digital (59, 135, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- digital (39, 77, 33)-net over F2, using
(136, 136+76, 86)-Net in Base 2 — Constructive
(136, 212, 86)-net in base 2, using
- trace code for nets [i] based on (30, 106, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
(136, 136+76, 124)-Net over F2 — Digital
Digital (136, 212, 124)-net over F2, using
(136, 136+76, 663)-Net in Base 2 — Upper bound on s
There is no (136, 212, 664)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6712 054214 895754 613962 772646 140686 213904 972613 721160 670667 477932 > 2212 [i]