MinT - Best Known (97−28, 97, s)-Nets in Base 3

Best Known (97−28, 97, s)-Nets in Base 3

(97−28, 97, 192)-Net over F₃ — Constructive and digital

Digital (69, 97, 192)-net over F₃, using

3¹ times duplication [i] based on digital (68, 96, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 32, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(97−28, 97, 284)-Net over F₃ — Digital

Digital (69, 97, 284)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−28, 97, 6098)-Net in Base 3 — Upper bound on s

There is no (69, 97, 6099)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19101 320112 506533 996538 575702 504231 160794 273133 > 3⁹⁷ [i]