MinT - Best Known (82, 82+49, s)-Nets in Base 9

Best Known (82, 82+49, s)-Nets in Base 9

(82, 82+49, 740)-Net over F₉ — Constructive and digital

Digital (82, 131, 740)-net over F₉, using

1 times m-reduction [i] based on digital (82, 132, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 66, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(82, 82+49, 966)-Net over F₉ — Digital

Digital (82, 131, 966)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+49, 180738)-Net in Base 9 — Upper bound on s

There is no (82, 131, 180739)-net in base 9, because

1 times m-reduction [i] would yield (82, 130, 180739)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11259 916467 000877 461509 178143 423403 016374 347368 623953 600681 072891 801334 493214 794081 518665 517038 537199 409176 097478 251449 032769 > 9¹³⁰ [i]