MinT - Best Known (180−50, 180, s)-Nets in Base 3

Best Known (180−50, 180, s)-Nets in Base 3

(180−50, 180, 282)-Net over F₃ — Constructive and digital

Digital (130, 180, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 60, 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]

(180−50, 180, 525)-Net over F₃ — Digital

Digital (130, 180, 525)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−50, 180, 13838)-Net in Base 3 — Upper bound on s

There is no (130, 180, 13839)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 192498 719583 211042 977041 798376 456028 474863 475042 025521 966820 163696 100483 092573 861359 > 3¹⁸⁰ [i]