MinT - Best Known (97−26, 97, s)-Nets in Base 3

Best Known (97−26, 97, s)-Nets in Base 3

Digital (71, 97, 228)-net over F₃, using

3¹ times duplication [i] based on digital (70, 96, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 32, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

Digital (71, 97, 374)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3⁹⁷, 374, F₃, 26) (dual of [374, 277, 27]-code), using
- 276 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (9, 5, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 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, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0) [i] based on linear OA(3²⁶, 27, F₃, 26) (dual of [27, 1, 27]-code or 27-arc in PG(25,3)), using
  - dual of repetition code with length 27 [i]

There is no (71, 97, 10278)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19088 875182 064485 248555 037335 494173 933858 088469 > 3⁹⁷ [i]