MinT - Best Known (8−5, 8, s)-Nets in Base 25

Best Known (8−5, 8, s)-Nets in Base 25

(8−5, 8, 300)-Net over F₂₅ — Constructive and digital

Digital (3, 8, 300)-net over F₂₅, using

25¹ times duplication [i] based on digital (2, 7, 300)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁷, 300, F₂₅, 5, 5) (dual of [(300, 5), 1493, 6]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
    - a code by Danev and Olsson [i]

(8−5, 8, 301)-Net over F₂₅ — Digital

Digital (3, 8, 301)-net over F₂₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(25⁸, 301, F₂₅, 2, 5) (dual of [(301, 2), 594, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25⁸, 602, F₂₅, 5) (dual of [602, 594, 6]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
    - a code by Danev and Olsson [i]

(8−5, 8, 4602)-Net in Base 25 — Upper bound on s

There is no (3, 8, 4603)-net in base 25, because

1 times m-reduction [i] would yield (3, 7, 4603)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 6103 578001 > 25⁷ [i]