MinT - Best Known (6, 6+10, s)-Nets in Base 3

Best Known (6, 6+10, s)-Nets in Base 3

(6, 6+10, 16)-Net over F₃ — Constructive and digital

Digital (6, 16, 16)-net over F₃, using

a shift-net [i]

(6, 6+10, 32)-Net over F₃ — Upper bound on s (digital)

There is no digital (6, 16, 33)-net over F₃, because

1 times m-reduction [i] would yield digital (6, 15, 33)-net over F₃, but
- extracting embedded orthogonal array [i] would yield linear OA(3¹⁵, 33, F₃, 9) (dual of [33, 18, 10]-code), but
  - â€œLPâ€ bound on codes from Brouwerâ€™s database [i]

(6, 6+10, 39)-Net in Base 3 — Upper bound on s

There is no (6, 16, 40)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 45 576657 > 3¹⁶ [i]