MinT - Best Known (59, 59+26, s)-Nets in Base 3

Best Known (59, 59+26, s)-Nets in Base 3

(59, 59+26, 144)-Net over F₃ — Constructive and digital

Digital (59, 85, 144)-net over F₃, using

3¹ times duplication [i] based on digital (58, 84, 144)-net over F₃, using
- trace code for nets [i] based on digital (2, 28, 48)-net over F₂₇, using
  - net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
      - a function field by GarcÃa and Quoos [i]

(59, 59+26, 211)-Net over F₃ — Digital

Digital (59, 85, 211)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+26, 3720)-Net in Base 3 — Upper bound on s

There is no (59, 85, 3721)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 36024 102290 149635 070152 342505 795228 395747 > 3⁸⁵ [i]