Best Known (202−75, 202, s)-Nets in Base 2
(202−75, 202, 69)-Net over F2 — Constructive and digital
Digital (127, 202, 69)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (39, 76, 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 (51, 126, 36)-net over F2, using
- net from sequence [i] based on digital (51, 35)-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 3 places 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 (51, 35)-sequence over F2, using
- digital (39, 76, 33)-net over F2, using
(202−75, 202, 72)-Net in Base 2 — Constructive
(127, 202, 72)-net in base 2, using
- trace code for nets [i] based on (26, 101, 36)-net in base 4, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- t-expansion [i] based on digital (51, 35)-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 3 places 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]
- t-expansion [i] based on digital (51, 35)-sequence over F2, using
- base expansion [i] based on digital (52, 35)-sequence over F2, using
- net from sequence [i] based on (26, 35)-sequence in base 4, using
(202−75, 202, 110)-Net over F2 — Digital
Digital (127, 202, 110)-net over F2, using
- trace code for nets [i] based on digital (26, 101, 55)-net over F4, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 26 and N(F) ≥ 55, using
- net from sequence [i] based on digital (26, 54)-sequence over F4, using
(202−75, 202, 579)-Net in Base 2 — Upper bound on s
There is no (127, 202, 580)-net in base 2, because
- 1 times m-reduction [i] would yield (127, 201, 580)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3 243224 710031 737376 034590 600666 439411 746786 703237 167521 434720 > 2201 [i]