MinT - Best Known (211−57, 211, s)-Nets in Base 3

Best Known (211−57, 211, s)-Nets in Base 3

(211−57, 211, 288)-Net over F₃ — Constructive and digital

Digital (154, 211, 288)-net over F₃, using

t-expansion [i] based on digital (153, 211, 288)-net over F₃, using
- 2 times m-reduction [i] based on digital (153, 213, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 71, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(211−57, 211, 663)-Net over F₃ — Digital

Digital (154, 211, 663)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−57, 211, 21371)-Net in Base 3 — Upper bound on s

There is no (154, 211, 21372)-net in base 3, because

1 times m-reduction [i] would yield (154, 210, 21372)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15703 346022 627767 930063 655542 246618 545460 810935 189354 461079 544754 115690 311883 853155 725822 092668 413121 > 3²¹⁰ [i]