MinT - Best Known (103−27, 103, s)-Nets in Base 3

Best Known (103−27, 103, s)-Nets in Base 3

(103−27, 103, 246)-Net over F₃ — Constructive and digital

Digital (76, 103, 246)-net over F₃, using

3¹ times duplication [i] based on digital (75, 102, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 34, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(103−27, 103, 422)-Net over F₃ — Digital

Digital (76, 103, 422)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(103−27, 103, 15689)-Net in Base 3 — Upper bound on s

There is no (76, 103, 15690)-net in base 3, because

1 times m-reduction [i] would yield (76, 102, 15690)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 641972 412198 528023 254632 756821 560616 216288 464157 > 3¹⁰² [i]