Best Known (121, 166, s)-Nets in Base 2
(121, 166, 138)-Net over F2 — Constructive and digital
Digital (121, 166, 138)-net over F2, using
- 21 times duplication [i] based on digital (120, 165, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 55, 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, 55, 46)-net over F8, using
(121, 166, 195)-Net over F2 — Digital
Digital (121, 166, 195)-net over F2, using
(121, 166, 1606)-Net in Base 2 — Upper bound on s
There is no (121, 166, 1607)-net in base 2, because
- 1 times m-reduction [i] would yield (121, 165, 1607)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 46 901867 819489 847341 970242 974991 651011 235172 695004 > 2165 [i]