Best Known (187−107, 187, s)-Nets in Base 2
(187−107, 187, 51)-Net over F2 — Constructive and digital
Digital (80, 187, 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]
(187−107, 187, 56)-Net over F2 — Digital
Digital (80, 187, 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
(187−107, 187, 165)-Net in Base 2 — Upper bound on s
There is no (80, 187, 166)-net in base 2, because
- 1 times m-reduction [i] would yield (80, 186, 166)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 100 967501 918636 023848 454676 269681 729797 634192 422395 488024 > 2186 [i]