Best Known (81, 81+115, s)-Nets in Base 2
(81, 81+115, 51)-Net over F2 — Constructive and digital
Digital (81, 196, 51)-net over F2, using
- t-expansion [i] based on digital (80, 196, 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
(81, 81+115, 56)-Net over F2 — Digital
Digital (81, 196, 56)-net over F2, using
- t-expansion [i] based on digital (80, 196, 56)-net over F2, using
- net from sequence [i] based on digital (80, 55)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 80 and N(F) ≥ 56, using
- net from sequence [i] based on digital (80, 55)-sequence over F2, using
(81, 81+115, 163)-Net in Base 2 — Upper bound on s
There is no (81, 196, 164)-net in base 2, because
- 1 times m-reduction [i] would yield (81, 195, 164)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 60676 546302 717958 463849 477888 982199 437580 913115 629514 089648 > 2195 [i]