MinT - Best Known (8, 12, s)-Nets in Base 5

Best Known (8, 12, s)-Nets in Base 5

(8, 12, 600)-Net over F₅ — Constructive and digital

Digital (8, 12, 600)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹², 600, F₅, 4, 4) (dual of [(600, 4), 2388, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(5¹², 600, F₅, 3, 4) (dual of [(600, 3), 1788, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(5¹², 1200, F₅, 4) (dual of [1200, 1188, 5]-code), using
    - trace code [i] based on linear OA(25⁶, 600, F₂₅, 4) (dual of [600, 594, 5]-code), using
      - 1 times truncation [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
        a code by Danev and Olsson [i]

(8, 12, 1200)-Net over F₅ — Digital

Digital (8, 12, 1200)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹², 1200, F₅, 4, 4) (dual of [(1200, 4), 4788, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(5¹², 1200, F₅, 3, 4) (dual of [(1200, 3), 3588, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹², 1200, F₅, 4) (dual of [1200, 1188, 5]-code), using
    - trace code [i] based on linear OA(25⁶, 600, F₂₅, 4) (dual of [600, 594, 5]-code), using
      - 1 times truncation [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
        a code by Danev and Olsson [i]

(8, 12, 5523)-Net in Base 5 — Upper bound on s

There is no (8, 12, 5524)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 244 204993 > 5¹² [i]