MinT - Best Known (179, 179+54, s)-Nets in Base 3

Best Known (179, 179+54, s)-Nets in Base 3

(179, 179+54, 600)-Net over F₃ — Constructive and digital

Digital (179, 233, 600)-net over F₃, using

3¹ times duplication [i] based on digital (178, 232, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 58, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(179, 179+54, 1314)-Net over F₃ — Digital

Digital (179, 233, 1314)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(179, 179+54, 71547)-Net in Base 3 — Upper bound on s

There is no (179, 233, 71548)-net in base 3, because

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]