Best Known (158, 158+102, s)-Nets in Base 2
(158, 158+102, 78)-Net over F2 — Constructive and digital
Digital (158, 260, 78)-net over F2, using
- 21 times duplication [i] based on digital (157, 259, 78)-net over F2, using
- t-expansion [i] based on digital (156, 259, 78)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (51, 102, 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 (54, 157, 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 (51, 102, 36)-net over F2, using
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (156, 259, 78)-net over F2, using
(158, 158+102, 84)-Net in Base 2 — Constructive
(158, 260, 84)-net in base 2, using
- t-expansion [i] based on (157, 260, 84)-net in base 2, using
- trace code for nets [i] based on (27, 130, 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, 130, 42)-net in base 4, using
(158, 158+102, 121)-Net over F2 — Digital
Digital (158, 260, 121)-net over F2, using
(158, 158+102, 607)-Net in Base 2 — Upper bound on s
There is no (158, 260, 608)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 897672 801215 722155 361402 713507 633928 813151 098587 820316 624418 880361 655624 753374 > 2260 [i]