MinT - Best Known (9, 9+5, s)-Nets in Base 2

Best Known (9, 9+5, s)-Nets in Base 2

(9, 9+5, 69)-Net over F₂ — Constructive and digital

Digital (9, 14, 69)-net over F₂, using

linear code embedding found in a computer search [i]

(9, 9+5, 124)-Net in Base 2 — Upper bound on s

There is no (9, 14, 125)-net in base 2, because

1 times m-reduction [i] would yield (9, 13, 125)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2¹³, 125, S₂, 4), but
  - the linear programming bound shows that MÂ â‰¥ 15 460480 / 1877 > 2¹³ [i]