Best Known (16, 31, s)-Nets in Base 2
(16, 31, 18)-Net over F2 — Constructive and digital
Digital (16, 31, 18)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (4, 11, 11)-net over F2, using
- digital (5, 20, 9)-net over F2, using
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 5 and N(F) ≥ 9, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
(16, 31, 47)-Net over F2 — Upper bound on s (digital)
There is no digital (16, 31, 48)-net over F2, because
- 1 times m-reduction [i] would yield digital (16, 30, 48)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(230, 48, F2, 14) (dual of [48, 18, 15]-code), but
- adding a parity check bit [i] would yield linear OA(231, 49, F2, 15) (dual of [49, 18, 16]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(230, 48, F2, 14) (dual of [48, 18, 15]-code), but
(16, 31, 56)-Net in Base 2 — Upper bound on s
There is no (16, 31, 57)-net in base 2, because
- 1 times m-reduction [i] would yield (16, 30, 57)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1126 764544 > 230 [i]