MinT - Best Known (6, 6+8, s)-Nets in Base 2

Best Known (6, 6+8, s)-Nets in Base 2

(6, 6+8, 15)-Net over F₂ — Constructive and digital

Digital (6, 14, 15)-net over F₂, using

linear code embedding found in a computer search [i]

(6, 6+8, 17)-Net over F₂ — Upper bound on s (digital)

There is no digital (6, 14, 18)-net over F₂, because

extracting embedded orthogonal array [i] would yield linear OA(2¹⁴, 18, F₂, 8) (dual of [18, 4, 9]-code), but
- Griesmer bound [i]

(6, 6+8, 18)-Net in Base 2 — Upper bound on s

There is no (6, 14, 19)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2¹⁴, 19, S₂, 2, 8), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 289742 490368 / 16 746765 > 2¹⁴ [i]