Best Known (228−66, 228, s)-Nets in Base 2
(228−66, 228, 138)-Net over F2 — Constructive and digital
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
(228−66, 228, 218)-Net over F2 — Digital
Digital (162, 228, 218)-net over F2, using
(228−66, 228, 1533)-Net in Base 2 — Upper bound on s
There is no (162, 228, 1534)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 434 506691 640692 579206 076656 895388 275764 916625 979116 207419 518221 353567 > 2228 [i]