MinT - Best Known (229−69, 229, s)-Nets in Base 3

Best Known (229−69, 229, s)-Nets in Base 3

(229−69, 229, 246)-Net over F₃ — Constructive and digital

Digital (160, 229, 246)-net over F₃, using

3¹ times duplication [i] based on digital (159, 228, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 76, 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]

(229−69, 229, 492)-Net over F₃ — Digital

Digital (160, 229, 492)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−69, 229, 10680)-Net in Base 3 — Upper bound on s

There is no (160, 229, 10681)-net in base 3, because

1 times m-reduction [i] would yield (160, 228, 10681)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 079109 407002 375008 939757 129698 962924 278728 943609 579671 349204 826056 396539 109928 035817 648522 298158 833427 189305 > 3²²⁸ [i]