Best Known (143−37, 143, s)-Nets in Base 2
(143−37, 143, 138)-Net over F2 — Constructive and digital
Digital (106, 143, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (106, 144, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 48, 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, 48, 46)-net over F8, using
(143−37, 143, 196)-Net over F2 — Digital
Digital (106, 143, 196)-net over F2, using
(143−37, 143, 1763)-Net in Base 2 — Upper bound on s
There is no (106, 143, 1764)-net in base 2, because
- 1 times m-reduction [i] would yield (106, 142, 1764)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 5 577304 085643 322424 523021 641640 786203 037214 > 2142 [i]