MinT - Best Known (115, 115+42, s)-Nets in Base 3

Best Known (115, 115+42, s)-Nets in Base 3

(115, 115+42, 282)-Net over F₃ — Constructive and digital

Digital (115, 157, 282)-net over F₃, using

3¹ times duplication [i] based on digital (114, 156, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 52, 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]

(115, 115+42, 539)-Net over F₃ — Digital

Digital (115, 157, 539)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+42, 15993)-Net in Base 3 — Upper bound on s

There is no (115, 157, 15994)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 809 209194 345864 615680 430292 894644 803763 569433 284854 175006 499070 457146 766637 > 3¹⁵⁷ [i]