Best Known (194−94, 194, s)-Nets in Base 2
(194−94, 194, 55)-Net over F2 — Constructive and digital
Digital (100, 194, 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]
(194−94, 194, 65)-Net over F2 — Digital
Digital (100, 194, 65)-net over F2, using
- t-expansion [i] based on digital (95, 194, 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
(194−94, 194, 217)-Net over F2 — Upper bound on s (digital)
There is no digital (100, 194, 218)-net over F2, because
- 2 times m-reduction [i] would yield digital (100, 192, 218)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(2192, 218, F2, 92) (dual of [218, 26, 93]-code), but
- 2 times code embedding in larger space [i] would yield linear OA(2194, 220, F2, 92) (dual of [220, 26, 93]-code), but
- adding a parity check bit [i] would yield linear OA(2195, 221, F2, 93) (dual of [221, 26, 94]-code), but
- 2 times code embedding in larger space [i] would yield linear OA(2194, 220, F2, 92) (dual of [220, 26, 93]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(2192, 218, F2, 92) (dual of [218, 26, 93]-code), but
(194−94, 194, 257)-Net in Base 2 — Upper bound on s
There is no (100, 194, 258)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 27659 720373 837776 883211 320505 037022 929276 914336 498339 654528 > 2194 [i]