MinT - Best Known (215−124, 215, s)-Nets in Base 3

Best Known (215−124, 215, s)-Nets in Base 3

(215−124, 215, 64)-Net over F₃ — Constructive and digital

Digital (91, 215, 64)-net over F₃, using

t-expansion [i] based on digital (89, 215, 64)-net over F₃, using
- net from sequence [i] based on digital (89, 63)-sequence over F₃, using
  - base reduction for sequences [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]

(215−124, 215, 96)-Net over F₃ — Digital

Digital (91, 215, 96)-net over F₃, using

t-expansion [i] based on digital (89, 215, 96)-net over F₃, using
- net from sequence [i] based on digital (89, 95)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 89 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₃ by Niederreiter/Xing [i]

(215−124, 215, 481)-Net in Base 3 — Upper bound on s

There is no (91, 215, 482)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 092920 154733 098534 813339 293980 160816 101313 524167 810349 735860 714624 642603 053556 279246 209927 687449 531821 > 3²¹⁵ [i]