MinT - Best Known (234−55, 234, s)-Nets in Base 3

Best Known (234−55, 234, s)-Nets in Base 3

(234−55, 234, 464)-Net over F₃ — Constructive and digital

Digital (179, 234, 464)-net over F₃, using

2 times m-reduction [i] based on digital (179, 236, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 59, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(234−55, 234, 1242)-Net over F₃ — Digital

Digital (179, 234, 1242)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−55, 234, 71547)-Net in Base 3 — Upper bound on s

There is no (179, 234, 71548)-net in base 3, because

1 times m-reduction [i] would yield (179, 233, 71548)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1476 730132 922073 952450 626800 617605 512563 104431 574672 744661 172588 994525 962697 155030 946990 660234 671387 157927 416145 > 3²³³ [i]