Best Known (11, 11+11, s)-Nets in Base 2
(11, 11+11, 22)-Net over F2 — Constructive and digital
(11, 11+11, 33)-Net over F2 — Upper bound on s (digital)
There is no digital (11, 22, 34)-net over F2, because
- 1 times m-reduction [i] would yield digital (11, 21, 34)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(221, 34, F2, 10) (dual of [34, 13, 11]-code), but
- adding a parity check bit [i] would yield linear OA(222, 35, F2, 11) (dual of [35, 13, 12]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(221, 34, F2, 10) (dual of [34, 13, 11]-code), but
(11, 11+11, 41)-Net in Base 2 — Upper bound on s
There is no (11, 22, 42)-net in base 2, because
- 1 times m-reduction [i] would yield (11, 21, 42)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 257410 > 221 [i]