Best Known (50, 100, s)-Nets in Base 2
(50, 100, 35)-Net over F2 — Constructive and digital
Digital (50, 100, 35)-net over F2, using
- t-expansion [i] based on digital (48, 100, 35)-net over F2, using
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (48, 34)-sequence over F2, using
(50, 100, 40)-Net over F2 — Digital
Digital (50, 100, 40)-net over F2, using
- net from sequence [i] based on digital (50, 39)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 50 and N(F) ≥ 40, using
(50, 100, 110)-Net over F2 — Upper bound on s (digital)
There is no digital (50, 100, 111)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2100, 111, F2, 50) (dual of [111, 11, 51]-code), but
(50, 100, 111)-Net in Base 2 — Upper bound on s
There is no (50, 100, 112)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(2100, 112, S2, 50), but
- the linear programming bound shows that M ≥ 552 695661 699508 019052 562597 543936 / 403 > 2100 [i]