Best Known (178, 178+74, s)-Nets in Base 2
(178, 178+74, 138)-Net over F2 — Constructive and digital
Digital (178, 252, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 84, 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
(178, 178+74, 229)-Net over F2 — Digital
Digital (178, 252, 229)-net over F2, using
(178, 178+74, 1590)-Net in Base 2 — Upper bound on s
There is no (178, 252, 1591)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 7262 484022 158468 742223 698509 259610 124522 883481 676197 923415 881958 977321 608660 > 2252 [i]