MinT - Best Known (231−73, 231, s)-Nets in Base 3

Best Known (231−73, 231, s)-Nets in Base 3

(231−73, 231, 192)-Net over F₃ — Constructive and digital

Digital (158, 231, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 77, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(231−73, 231, 427)-Net over F₃ — Digital

Digital (158, 231, 427)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−73, 231, 7944)-Net in Base 3 — Upper bound on s

There is no (158, 231, 7945)-net in base 3, because

1 times m-reduction [i] would yield (158, 230, 7945)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 890786 380419 024745 049995 023898 416888 738336 659818 617433 091046 155291 529596 572571 061226 525300 906299 470547 782289 > 3²³⁰ [i]