MinT - Best Known (71, 71+20, s)-Nets in Base 3

Best Known (71, 71+20, s)-Nets in Base 3

(71, 71+20, 464)-Net over F₃ — Constructive and digital

Digital (71, 91, 464)-net over F₃, using

1 times m-reduction [i] based on digital (71, 92, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 23, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(71, 71+20, 901)-Net over F₃ — Digital

Digital (71, 91, 901)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3⁹¹, 901, F₃, 20) (dual of [901, 810, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁹¹, 1093, F₃, 20) (dual of [1093, 1002, 21]-code), using
  - the BCH-code C(I) with length 1093Â | 3⁷âˆ’1, defining interval IÂ =Â {1,3,5,…,39}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

(71, 71+20, 49735)-Net in Base 3 — Upper bound on s

There is no (71, 91, 49736)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 186343 543529 649702 937810 598414 863365 449137 > 3⁹¹ [i]