Best Known (242−70, 242, s)-Nets in Base 2
(242−70, 242, 138)-Net over F2 — Constructive and digital
Digital (172, 242, 138)-net over F2, using
- 1 times m-reduction [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
(242−70, 242, 229)-Net over F2 — Digital
Digital (172, 242, 229)-net over F2, using
(242−70, 242, 1626)-Net in Base 2 — Upper bound on s
There is no (172, 242, 1627)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 7 177418 846187 039965 453079 677101 992297 025345 095875 118599 814530 000138 667068 > 2242 [i]