MinT - Best Known (246−107, 246, s)-Nets in Base 3

Best Known (246−107, 246, s)-Nets in Base 3

(246−107, 246, 128)-Net over F₃ — Constructive and digital

Digital (139, 246, 128)-net over F₃, using

t-expansion [i] based on digital (138, 246, 128)-net over F₃, using
- 4 times m-reduction [i] based on digital (138, 250, 128)-net over F₃, using
  - trace code for nets [i] based on digital (13, 125, 64)-net over F₉, using
    - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
        a function field by GarcÃa and Quoos [i]

(246−107, 246, 177)-Net over F₃ — Digital

Digital (139, 246, 177)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−107, 246, 1601)-Net in Base 3 — Upper bound on s

There is no (139, 246, 1602)-net in base 3, because

1 times m-reduction [i] would yield (139, 245, 1602)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 800 751130 174735 293027 944821 737305 372388 787745 518188 788653 820582 915798 462808 389172 904658 167634 818866 508888 251802 897341 > 3²⁴⁵ [i]