Best Known (244−71, 244, s)-Nets in Base 2
(244−71, 244, 138)-Net over F2 — Constructive and digital
Digital (173, 244, 138)-net over F2, using
- 21 times duplication [i] based on digital (172, 243, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 81, 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, 81, 46)-net over F8, using
(244−71, 244, 227)-Net over F2 — Digital
Digital (173, 244, 227)-net over F2, using
(244−71, 244, 1659)-Net in Base 2 — Upper bound on s
There is no (173, 244, 1660)-net in base 2, because
- 1 times m-reduction [i] would yield (173, 243, 1660)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 14 193008 462762 997570 556275 358268 640351 257491 089574 579043 065218 988247 945559 > 2243 [i]