Best Known (122, 122+45, s)-Nets in Base 2
(122, 122+45, 138)-Net over F2 — Constructive and digital
Digital (122, 167, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (122, 168, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 56, 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, 56, 46)-net over F8, using
(122, 122+45, 199)-Net over F2 — Digital
Digital (122, 167, 199)-net over F2, using
(122, 122+45, 1659)-Net in Base 2 — Upper bound on s
There is no (122, 167, 1660)-net in base 2, because
- 1 times m-reduction [i] would yield (122, 166, 1660)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 94 465603 267894 192988 431704 786946 906138 496970 680358 > 2166 [i]