MinT - Best Known (157, 222, s)-Nets in Base 3

Best Known (157, 222, s)-Nets in Base 3

(157, 222, 264)-Net over F₃ — Constructive and digital

Digital (157, 222, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 74, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(157, 222, 525)-Net over F₃ — Digital

Digital (157, 222, 525)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157, 222, 12585)-Net in Base 3 — Upper bound on s

There is no (157, 222, 12586)-net in base 3, because

1 times m-reduction [i] would yield (157, 221, 12586)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2779 060489 528000 017566 617851 758201 290619 333034 877621 937188 780689 062815 346038 512447 816378 234676 214998 642497 > 3²²¹ [i]