Best Known (200−96, 200, s)-Nets in Base 2
(200−96, 200, 55)-Net over F2 — Constructive and digital
Digital (104, 200, 55)-net over F2, using
- t-expansion [i] based on digital (100, 200, 55)-net over F2, using
- net from sequence [i] based on digital (100, 54)-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 6 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 (100, 54)-sequence over F2, using
(200−96, 200, 65)-Net over F2 — Digital
Digital (104, 200, 65)-net over F2, using
- t-expansion [i] based on digital (95, 200, 65)-net over F2, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
- net from sequence [i] based on digital (95, 64)-sequence over F2, using
(200−96, 200, 236)-Net over F2 — Upper bound on s (digital)
There is no digital (104, 200, 237)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(2200, 237, F2, 96) (dual of [237, 37, 97]-code), but
- residual code [i] would yield OA(2104, 140, S2, 48), but
- the linear programming bound shows that M ≥ 906615 640616 170781 657520 759485 197602 258944 / 38102 739675 > 2104 [i]
- residual code [i] would yield OA(2104, 140, S2, 48), but
(200−96, 200, 271)-Net in Base 2 — Upper bound on s
There is no (104, 200, 272)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 776897 368061 762038 877905 395932 431812 469269 318035 980551 190640 > 2200 [i]