MinT - Best Known (76, 98, s)-Nets in Base 3

Best Known (76, 98, s)-Nets in Base 3

(76, 98, 464)-Net over F₃ — Constructive and digital

Digital (76, 98, 464)-net over F₃, using

3² times duplication [i] based on digital (74, 96, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 24, 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]

(76, 98, 838)-Net over F₃ — Digital

Digital (76, 98, 838)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3⁹⁸, 838, F₃, 22) (dual of [838, 740, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁹⁸, 1093, F₃, 22) (dual of [1093, 995, 23]-code), using
  - the BCH-code C(I) with length 1093Â | 3⁷âˆ’1, defining interval IÂ =Â {1,57,113,…,84}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]

(76, 98, 43711)-Net in Base 3 — Upper bound on s

There is no (76, 98, 43712)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 57270 235552 376952 615888 110389 136937 039719 254785 > 3⁹⁸ [i]