Best Known (84, 166, s)-Nets in Base 2
(84, 166, 51)-Net over F2 — Constructive and digital
Digital (84, 166, 51)-net over F2, using
- t-expansion [i] based on digital (80, 166, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-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 2 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 (80, 50)-sequence over F2, using
(84, 166, 57)-Net over F2 — Digital
Digital (84, 166, 57)-net over F2, using
- t-expansion [i] based on digital (83, 166, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(84, 166, 186)-Net over F2 — Upper bound on s (digital)
There is no digital (84, 166, 187)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2166, 187, F2, 82) (dual of [187, 21, 83]-code), but
- residual code [i] would yield linear OA(284, 104, F2, 41) (dual of [104, 20, 42]-code), but
- “Bro†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(284, 104, F2, 41) (dual of [104, 20, 42]-code), but
(84, 166, 211)-Net in Base 2 — Upper bound on s
There is no (84, 166, 212)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 96 566697 296403 102515 495902 319018 075759 398818 418620 > 2166 [i]