MinT - Best Known (82, 82+61, s)-Nets in Base 9

Best Known (82, 82+61, s)-Nets in Base 9

(82, 82+61, 344)-Net over F₉ — Constructive and digital

Digital (82, 143, 344)-net over F₉, using

7 times m-reduction [i] based on digital (82, 150, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 75, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(82, 82+61, 536)-Net over F₉ — Digital

Digital (82, 143, 536)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+61, 49463)-Net in Base 9 — Upper bound on s

There is no (82, 143, 49464)-net in base 9, because

1 times m-reduction [i] would yield (82, 142, 49464)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3180 696159 174986 211064 731080 007128 578113 959789 951591 009039 966203 659063 851142 515021 437932 576030 724590 757174 144460 373222 677158 081361 551745 > 9¹⁴² [i]