Best Known (157, 157+97, s)-Nets in Base 2
(157, 157+97, 84)-Net over F2 — Constructive and digital
Digital (157, 254, 84)-net over F2, using
- 1 times m-reduction [i] based on digital (157, 255, 84)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (54, 103, 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 (54, 152, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2 (see above)
- digital (54, 103, 42)-net over F2, using
- (u, u+v)-construction [i] based on
(157, 157+97, 86)-Net in Base 2 — Constructive
(157, 254, 86)-net in base 2, using
- trace code for nets [i] based on (30, 127, 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
(157, 157+97, 126)-Net over F2 — Digital
Digital (157, 254, 126)-net over F2, using
(157, 157+97, 655)-Net in Base 2 — Upper bound on s
There is no (157, 254, 656)-net in base 2, because
- 1 times m-reduction [i] would yield (157, 253, 656)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 15346 507038 641583 700091 438643 866490 004373 083244 124849 355541 775069 308675 951672 > 2253 [i]