MinT - Best Known (170, 170+71, s)-Nets in Base 3

Best Known (170, 170+71, s)-Nets in Base 3

(170, 170+71, 264)-Net over F₃ — Constructive and digital

Digital (170, 241, 264)-net over F₃, using

3¹ times duplication [i] based on digital (169, 240, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 80, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(170, 170+71, 553)-Net over F₃ — Digital

Digital (170, 241, 553)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(170, 170+71, 12964)-Net in Base 3 — Upper bound on s

There is no (170, 241, 12965)-net in base 3, because

1 times m-reduction [i] would yield (170, 240, 12965)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 230020 155323 350685 203033 826658 350423 541661 090409 566856 828830 325991 152880 967926 428821 589548 995969 216150 065920 625643 > 3²⁴⁰ [i]