Best Known (242−137, 242, s)-Nets in Base 2
(242−137, 242, 56)-Net over F2 — Constructive and digital
Digital (105, 242, 56)-net over F2, using
- net from sequence [i] based on digital (105, 55)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 7 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(242−137, 242, 65)-Net over F2 — Digital
Digital (105, 242, 65)-net over F2, using
- t-expansion [i] based on digital (95, 242, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(242−137, 242, 216)-Net in Base 2 — Upper bound on s
There is no (105, 242, 217)-net in base 2, because
- 1 times m-reduction [i] would yield (105, 241, 217)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3 755615 820535 306690 121791 715269 637751 176938 020352 865891 600807 384792 242630 > 2241 [i]