MinT - Best Known (3, 8, s)-Nets in Base 81

Best Known (3, 8, s)-Nets in Base 81

Digital (3, 8, 3240)-net over F₈₁, using

81¹ times duplication [i] based on digital (2, 7, 3240)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81⁷, 3240, F₈₁, 5, 5) (dual of [(3240, 5), 16193, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(81⁷, 3240, F₈₁, 4, 5) (dual of [(3240, 4), 12953, 6]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
      - a code by Danev and Olsson [i]

Digital (3, 8, 3241)-net over F₈₁, using

There is no (3, 8, 84552)-net in base 81, because

1 times m-reduction [i] would yield (3, 7, 84552)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 22 877214 347521 > 81⁷ [i]