MinT - Best Known (15−5, 15, s)-Nets in Base 5

Best Known (15−5, 15, s)-Nets in Base 5

Digital (10, 15, 601)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹⁵, 601, F₅, 5, 5) (dual of [(601, 5), 2990, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(5¹⁵, 1203, F₅, 5) (dual of [1203, 1188, 6]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(5¹⁴, 1202, F₅, 5) (dual of [1202, 1188, 6]-code), using
    - trace code [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
      - a code by Danev and Olsson [i]

Digital (10, 15, 829)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5¹⁵, 829, F₅, 5) (dual of [829, 814, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(5¹⁵, 1203, F₅, 5) (dual of [1203, 1188, 6]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(5¹⁴, 1202, F₅, 5) (dual of [1202, 1188, 6]-code), using
    - trace code [i] based on linear OA(25⁷, 601, F₂₅, 5) (dual of [601, 594, 6]-code), using
      - a code by Danev and Olsson [i]

There is no (10, 15, 27621)-net in base 5, because

1 times m-reduction [i] would yield (10, 14, 27621)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 6103 799065 > 5¹⁴ [i]