MinT - Best Known (101−13, 101, s)-Nets in Base 5

Best Known (101−13, 101, s)-Nets in Base 5

Digital (88, 101, 1398100)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹⁰¹, 1398100, F₅, 13, 13) (dual of [(1398100, 13), 18175199, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(5¹⁰¹, 8388601, F₅, 13) (dual of [8388601, 8388500, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁰¹, large, F₅, 13) (dual of [large, large−101, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (88, 101, 4194301)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5¹⁰¹, 4194301, F₅, 2, 13) (dual of [(4194301, 2), 8388501, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹⁰¹, 8388602, F₅, 13) (dual of [8388602, 8388501, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹⁰¹, large, F₅, 13) (dual of [large, large−101, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (88, 101, large)-net in base 5, because

11 times m-reduction [i] would yield (88, 90, large)-net in base 5, but
- mutually orthogonal hypercube bound [i]