MinT - Best Known (88−24, 88, s)-Nets in Base 3

Best Known (88−24, 88, s)-Nets in Base 3

Digital (64, 88, 204)-net over F₃, using

3¹ times duplication [i] based on digital (63, 87, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 29, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

Digital (64, 88, 327)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3⁸⁸, 327, F₃, 24) (dual of [327, 239, 25]-code), using
- 238 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (8, 5, 3, 2, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0) [i] based on linear OA(3²⁴, 25, F₃, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,3)), using
  - dual of repetition code with length 25 [i]

There is no (64, 88, 8330)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 970395 296062 712739 438136 274903 308140 895609 > 3⁸⁸ [i]