MinT - Best Known (220−62, 220, s)-Nets in Base 3

Best Known (220−62, 220, s)-Nets in Base 3

(220−62, 220, 288)-Net over F₃ — Constructive and digital

Digital (158, 220, 288)-net over F₃, using

3¹ times duplication [i] based on digital (157, 219, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 73, 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]

(220−62, 220, 592)-Net over F₃ — Digital

Digital (158, 220, 592)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−62, 220, 15071)-Net in Base 3 — Upper bound on s

There is no (158, 220, 15072)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 927 682476 164367 505281 983857 795440 781157 814438 825197 280334 649328 611312 662449 347339 673294 326735 523622 703745 > 3²²⁰ [i]