MinT - Best Known (8, 8+8, s)-Nets in Base 3

Best Known (8, 8+8, s)-Nets in Base 3

(8, 8+8, 22)-Net over F₃ — Constructive and digital

Digital (8, 16, 22)-net over F₃, using

3² times duplication [i] based on digital (6, 14, 22)-net over F₃, using
- linear code embedding found in a computer search [i]

(8, 8+8, 23)-Net over F₃ — Digital

Digital (8, 16, 23)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(3¹⁶, 23, F₃, 2, 8) (dual of [(23, 2), 30, 9]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁴, 22, F₃, 2, 8) (dual of [(22, 2), 30, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (6, 14, 22)-net over F₃, using
    - linear code embedding found in a computer search [i]

(8, 8+8, 86)-Net in Base 3 — Upper bound on s

There is no (8, 16, 87)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 44 609657 > 3¹⁶ [i]