MinT - Best Known (230−101, 230, s)-Nets in Base 3

Best Known (230−101, 230, s)-Nets in Base 3

(230−101, 230, 128)-Net over F₃ — Constructive and digital

Digital (129, 230, 128)-net over F₃, using

2 times m-reduction [i] based on digital (129, 232, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 116, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(230−101, 230, 163)-Net over F₃ — Digital

Digital (129, 230, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−101, 230, 1443)-Net in Base 3 — Upper bound on s

There is no (129, 230, 1444)-net in base 3, because

1 times m-reduction [i] would yield (129, 229, 1444)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 574084 830267 480961 940472 477086 556655 222823 698468 159625 101541 399317 347985 428301 955148 299078 025553 910355 142137 > 3²²⁹ [i]