MinT - Best Known (9, 9+5, s)-Nets in Base 3

Best Known (9, 9+5, s)-Nets in Base 3

(9, 9+5, 103)-Net over F₃ — Constructive and digital

Digital (9, 14, 103)-net over F₃, using

3¹ times duplication [i] based on digital (8, 13, 103)-net over F₃, using
- linear code embedding found in a computer search [i]

(9, 9+5, 104)-Net over F₃ — Digital

Digital (9, 14, 104)-net over F₃, using

net defined by OOA [i] based on linear OOA(3¹⁴, 104, F₃, 5, 5) (dual of [(104, 5), 506, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(3¹⁴, 104, F₃, 4, 5) (dual of [(104, 4), 402, 6]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁴, 104, F₃, 5) (dual of [104, 90, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁴, 146, F₃, 5) (dual of [146, 132, 6]-code), using
      - trace code [i] based on linear OA(9⁷, 73, F₉, 5) (dual of [73, 66, 6]-code), using
        a code by Danev and Olsson [i]

(9, 9+5, 891)-Net in Base 3 — Upper bound on s

There is no (9, 14, 892)-net in base 3, because

1 times m-reduction [i] would yield (9, 13, 892)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 596681 > 3¹³ [i]