MinT - Best Known (106, 142, s)-Nets in Base 3

Best Known (106, 142, s)-Nets in Base 3

(106, 142, 288)-Net over F₃ — Constructive and digital

Digital (106, 142, 288)-net over F₃, using

3¹ times duplication [i] based on digital (105, 141, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 47, 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]

(106, 142, 615)-Net over F₃ — Digital

Digital (106, 142, 615)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 142, 21913)-Net in Base 3 — Upper bound on s

There is no (106, 142, 21914)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 419193 002366 793360 231687 566611 772076 485236 893005 426725 817214 204805 > 3¹⁴² [i]