Best Known (144−63, 144, s)-Nets in Base 2
(144−63, 144, 51)-Net over F2 — Constructive and digital
Digital (81, 144, 51)-net over F2, using
- t-expansion [i] based on digital (80, 144, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 2 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (80, 50)-sequence over F2, using
(144−63, 144, 58)-Net over F2 — Digital
Digital (81, 144, 58)-net over F2, using
(144−63, 144, 260)-Net in Base 2 — Upper bound on s
There is no (81, 144, 261)-net in base 2, because
- 1 times m-reduction [i] would yield (81, 143, 261)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 11 399570 023240 818706 227890 417730 201177 579776 > 2143 [i]