MinT - Best Known (8, 8+4, s)-Nets in Base 8

Best Known (8, 8+4, s)-Nets in Base 8

(8, 8+4, 4032)-Net over F₈ — Constructive and digital

Digital (8, 12, 4032)-net over F₈, using

net defined by OOA [i] based on linear OOA(8¹², 4032, F₈, 4, 4) (dual of [(4032, 4), 16116, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(8¹², 4032, F₈, 3, 4) (dual of [(4032, 3), 12084, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(8¹², 8064, F₈, 4) (dual of [8064, 8052, 5]-code), using
    - trace code [i] based on linear OA(64⁶, 4032, F₆₄, 4) (dual of [4032, 4026, 5]-code), using
      - 1 times truncation [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]

(8, 8+4, 8064)-Net over F₈ — Digital

Digital (8, 12, 8064)-net over F₈, using

net defined by OOA [i] based on linear OOA(8¹², 8064, F₈, 4, 4) (dual of [(8064, 4), 32244, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(8¹², 8064, F₈, 3, 4) (dual of [(8064, 3), 24180, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹², 8064, F₈, 4) (dual of [8064, 8052, 5]-code), using
    - trace code [i] based on linear OA(64⁶, 4032, F₆₄, 4) (dual of [4032, 4026, 5]-code), using
      - 1 times truncation [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]

(8, 8+4, 52960)-Net in Base 8 — Upper bound on s

There is no (8, 12, 52961)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 68721 293264 > 8¹² [i]