Best Known (239−69, 239, s)-Nets in Base 2
(239−69, 239, 138)-Net over F2 — Constructive and digital
Digital (170, 239, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (170, 240, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 80, 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, 80, 46)-net over F8, using
(239−69, 239, 228)-Net over F2 — Digital
Digital (170, 239, 228)-net over F2, using
(239−69, 239, 1682)-Net in Base 2 — Upper bound on s
There is no (170, 239, 1683)-net in base 2, because
- 1 times m-reduction [i] would yield (170, 238, 1683)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 444213 827584 636440 205243 931843 842733 699400 854773 969149 844573 265082 516148 > 2238 [i]