MinT - Best Known (121−26, 121, s)-Nets in Base 5

Best Known (121−26, 121, s)-Nets in Base 5

Digital (95, 121, 1201)-net over F₅, using

net defined by OOA [i] based on linear OOA(5¹²¹, 1201, F₅, 26, 26) (dual of [(1201, 26), 31105, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5¹²¹, 15613, F₅, 26) (dual of [15613, 15492, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹²¹, 15625, F₅, 26) (dual of [15625, 15504, 27]-code), using
    - an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

Digital (95, 121, 7812)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(5¹²¹, 7812, F₅, 2, 26) (dual of [(7812, 2), 15503, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5¹²¹, 15624, F₅, 26) (dual of [15624, 15503, 27]-code), using
  - discarding factors / shortening the dual code based on linear OA(5¹²¹, 15625, F₅, 26) (dual of [15625, 15504, 27]-code), using
    - an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 15624Â = 5⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]

There is no (95, 121, 4540912)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 761587 640384 984632 269583 286654 317029 197140 466868 503192 513175 248877 524347 622196 197825 > 5¹²¹ [i]