MinT - Best Known (70, 70+24, s)-Nets in Base 3

Best Known (70, 70+24, s)-Nets in Base 3

Digital (70, 94, 246)-net over F₃, using

3¹ times duplication [i] based on digital (69, 93, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 31, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

Digital (70, 94, 432)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3⁹⁴, 432, F₃, 24) (dual of [432, 338, 25]-code), using
- 337 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, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 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 (70, 94, 14436)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 707 186623 631413 514559 472344 243890 002054 819073 > 3⁹⁴ [i]