Best Known (80, 80+102, s)-Nets in Base 2
(80, 80+102, 51)-Net over F2 — Constructive and digital
Digital (80, 182, 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]
(80, 80+102, 56)-Net over F2 — Digital
Digital (80, 182, 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
(80, 80+102, 169)-Net in Base 2 — Upper bound on s
There is no (80, 182, 170)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 7 427620 789554 934442 017005 852950 062741 775419 889511 942848 > 2182 [i]