Best Known (92, 207, s)-Nets in Base 2
(92, 207, 53)-Net over F2 — Constructive and digital
Digital (92, 207, 53)-net over F2, using
- t-expansion [i] based on digital (90, 207, 53)-net over F2, using
- net from sequence [i] based on digital (90, 52)-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 4 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]
- net from sequence [i] based on digital (90, 52)-sequence over F2, using
(92, 207, 60)-Net over F2 — Digital
Digital (92, 207, 60)-net over F2, using
- net from sequence [i] based on digital (92, 59)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 92 and N(F) ≥ 60, using
(92, 207, 193)-Net over F2 — Upper bound on s (digital)
There is no digital (92, 207, 194)-net over F2, because
- 19 times m-reduction [i] would yield digital (92, 188, 194)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2188, 194, F2, 96) (dual of [194, 6, 97]-code), but
(92, 207, 195)-Net in Base 2 — Upper bound on s
There is no (92, 207, 196)-net in base 2, because
- 1 times m-reduction [i] would yield (92, 206, 196)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 106 883936 880518 525032 533687 500929 780512 817842 645193 787804 634632 > 2206 [i]