Best Known (229−66, 229, s)-Nets in Base 2
(229−66, 229, 138)-Net over F2 — Constructive and digital
Digital (163, 229, 138)-net over F2, using
- 21 times duplication [i] based on digital (162, 228, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 76, 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
- trace code for nets [i] based on digital (10, 76, 46)-net over F8, using
(229−66, 229, 221)-Net over F2 — Digital
Digital (163, 229, 221)-net over F2, using
(229−66, 229, 1567)-Net in Base 2 — Upper bound on s
There is no (163, 229, 1568)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 876 621943 712172 896314 665866 941540 021623 147897 392779 117223 787978 441840 > 2229 [i]