MinT - Best Known (9, 9+10, s)-Nets in Base 2

Best Known (9, 9+10, s)-Nets in Base 2

(9, 9+10, 17)-Net over F₂ — Constructive and digital

Digital (9, 19, 17)-net over F₂, using

linear code embedding found in a computer search [i]

(9, 9+10, 26)-Net over F₂ — Upper bound on s (digital)

There is no digital (9, 19, 27)-net over F₂, because

extracting embedded orthogonal array [i] would yield linear OA(2¹⁹, 27, F₂, 10) (dual of [27, 8, 11]-code), but
- adding a parity check bit [i] would yield linear OA(2²⁰, 28, F₂, 11) (dual of [28, 8, 12]-code), but
  - â€œDMâ€ bound on codes from Brouwerâ€™s database [i]

(9, 9+10, 28)-Net in Base 2 — Upper bound on s

There is no (9, 19, 29)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2¹⁹, 29, S₂, 2, 10), but
- the linear programming bound for OOAs shows that MÂ â‰¥ 2780 170958 083671 387775 959040 / 5028 625285 594383 279177 > 2¹⁹ [i]