Best Known (6, 11, s)-Nets in Base 2
(6, 11, 26)-Net over F2 — Constructive and digital
Digital (6, 11, 26)-net over F2, using
(6, 11, 33)-Net over F2 — Upper bound on s (digital)
There is no digital (6, 11, 34)-net over F2, because
- 1 times m-reduction [i] would yield digital (6, 10, 34)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(210, 34, F2, 4) (dual of [34, 24, 5]-code), but
- “BoV†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(210, 34, F2, 4) (dual of [34, 24, 5]-code), but
(6, 11, 42)-Net in Base 2 — Upper bound on s
There is no (6, 11, 43)-net in base 2, because
- 1 times m-reduction [i] would yield (6, 10, 43)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1033 > 210 [i]
- extracting embedded orthogonal array [i] would yield OA(210, 43, S2, 4), but
- the linear programming bound shows that M ≥ 74880 / 73 > 210 [i]