MinT - Best Known (88−26, 88, s)-Nets in Base 3

Best Known (88−26, 88, s)-Nets in Base 3

(88−26, 88, 156)-Net over F₃ — Constructive and digital

Digital (62, 88, 156)-net over F₃, using

3¹ times duplication [i] based on digital (61, 87, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 29, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(88−26, 88, 244)-Net over F₃ — Digital

Digital (62, 88, 244)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88−26, 88, 4797)-Net in Base 3 — Upper bound on s

There is no (62, 88, 4798)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 971776 774604 453632 089050 421942 891673 023621 > 3⁸⁸ [i]