MinT - Best Known (10, 10+8, s)-Nets in Base 2

Best Known (10, 10+8, s)-Nets in Base 2

(10, 10+8, 26)-Net over F₂ — Constructive and digital

Digital (10, 18, 26)-net over F₂, using

linear code embedding found in a computer search [i]

(10, 10+8, 34)-Net over F₂ — Upper bound on s (digital)

There is no digital (10, 18, 35)-net over F₂, because

extracting embedded orthogonal array [i] would yield linear OA(2¹⁸, 35, F₂, 8) (dual of [35, 17, 9]-code), but
- â€œJaâ€ bound on codes from Brouwerâ€™s database [i]

(10, 10+8, 44)-Net in Base 2 — Upper bound on s

There is no (10, 18, 45)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 265831 > 2¹⁸ [i]