MinT - Best Known (70, 152, s)-Nets in Base 3

Best Known (70, 152, s)-Nets in Base 3

(70, 152, 52)-Net over F₃ — Constructive and digital

Digital (70, 152, 52)-net over F₃, using

2 times m-reduction [i] based on digital (70, 154, 52)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 55, 24)-net over F₃, using
    - net from sequence [i] based on digital (13, 23)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
  2. digital (15, 99, 28)-net over F₃, using
    - net from sequence [i] based on digital (15, 27)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
        an explicitly constructive algebraic function field [i]

(70, 152, 82)-Net over F₃ — Digital

Digital (70, 152, 82)-net over F₃, using

t-expansion [i] based on digital (69, 152, 82)-net over F₃, using
- net from sequence [i] based on digital (69, 81)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 69 and N(F) ≥ 82, using
    - Drinfeld modules of rank 1 [i]

(70, 152, 434)-Net in Base 3 — Upper bound on s

There is no (70, 152, 435)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 382628 804145 737445 334527 981359 135753 222641 895891 682483 947239 097142 153687 > 3¹⁵² [i]