Best Known (245−71, 245, s)-Nets in Base 2
(245−71, 245, 138)-Net over F2 — Constructive and digital
Digital (174, 245, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (174, 246, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 82, 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, 82, 46)-net over F8, using
(245−71, 245, 231)-Net over F2 — Digital
Digital (174, 245, 231)-net over F2, using
(245−71, 245, 1694)-Net in Base 2 — Upper bound on s
There is no (174, 245, 1695)-net in base 2, because
- 1 times m-reduction [i] would yield (174, 244, 1695)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 28 836555 940262 590159 569262 804333 810463 802994 613702 622625 867856 990018 341336 > 2244 [i]