MinT - Best Known (17, 21, s)-Nets in Base 4

Best Known (17, 21, s)-Nets in Base 4

Digital (17, 21, 349525)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²¹, 349525, F₄, 4, 4) (dual of [(349525, 4), 1398079, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4²¹, 349525, F₄, 3, 4) (dual of [(349525, 3), 1048554, 5]-NRT-code), using
  - OA 2-folding and stacking [i] based on linear OA(4²¹, 699050, F₄, 4) (dual of [699050, 699029, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²¹, 699051, F₄, 4) (dual of [699051, 699030, 5]-code), using
      - quaternary constacyclic codes with minimum distance 5 [i]

Digital (17, 21, 494303)-net over F₄, using

net defined by OOA [i] based on linear OOA(4²¹, 494303, F₄, 4, 4) (dual of [(494303, 4), 1977191, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(4²¹, 494303, F₄, 3, 4) (dual of [(494303, 3), 1482888, 5]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(4²¹, 494303, F₄, 4) (dual of [494303, 494282, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²¹, 699051, F₄, 4) (dual of [699051, 699030, 5]-code), using
      - quaternary constacyclic codes with minimum distance 5 [i]

There is no (17, 21, 988606)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4 398048 584926 > 4²¹ [i]