Best Known (118, 118+43, s)-Nets in Base 2
(118, 118+43, 138)-Net over F2 — Constructive and digital
Digital (118, 161, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (118, 162, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 54, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- trace code for nets [i] based on digital (10, 54, 46)-net over F8, using
(118, 118+43, 198)-Net over F2 — Digital
Digital (118, 161, 198)-net over F2, using
(118, 118+43, 1675)-Net in Base 2 — Upper bound on s
There is no (118, 161, 1676)-net in base 2, because
- 1 times m-reduction [i] would yield (118, 160, 1676)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 469610 172794 114269 750221 871028 653078 082170 567792 > 2160 [i]