MinT - Best Known (163−44, 163, s)-Nets in Base 3

Best Known (163−44, 163, s)-Nets in Base 3

(163−44, 163, 282)-Net over F₃ — Constructive and digital

Digital (119, 163, 282)-net over F₃, using

3¹ times duplication [i] based on digital (118, 162, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 54, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(163−44, 163, 537)-Net over F₃ — Digital

Digital (119, 163, 537)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−44, 163, 15497)-Net in Base 3 — Upper bound on s

There is no (119, 163, 15498)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 590466 961645 396543 058924 911246 334305 008806 548269 903090 896731 984119 863210 519437 > 3¹⁶³ [i]