Best Known (90, 90+29, s)-Nets in Base 2
(90, 90+29, 138)-Net over F2 — Constructive and digital
Digital (90, 119, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (90, 120, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 40, 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, 40, 46)-net over F8, using
(90, 90+29, 197)-Net over F2 — Digital
Digital (90, 119, 197)-net over F2, using
(90, 90+29, 2062)-Net in Base 2 — Upper bound on s
There is no (90, 119, 2063)-net in base 2, because
- 1 times m-reduction [i] would yield (90, 118, 2063)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 332993 577174 430156 208210 118965 125437 > 2118 [i]