MinT - Best Known (73, 100, s)-Nets in Base 3

Best Known (73, 100, s)-Nets in Base 3

Digital (73, 100, 228)-net over F₃, using

3¹ times duplication [i] based on digital (72, 99, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 33, 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 (73, 100, 374)-net over F₃, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(3¹⁰⁰, 374, F₃, 27) (dual of [374, 274, 28]-code), using
- 273 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (9, 5, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 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, 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, 4 times 0, 1, 5 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, 8 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, 12 times 0, 1, 13 times 0) [i] based on linear OA(3²⁷, 28, F₃, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
  - dual of repetition code with length 28 [i]

There is no (73, 100, 12173)-net in base 3, because

1 times m-reduction [i] would yield (73, 99, 12173)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 171818 823267 643994 158331 689822 901371 477741 592971 > 3⁹⁹ [i]