MinT - Best Known (82−46, 82, s)-Nets in Base 9

Best Known (82−46, 82, s)-Nets in Base 9

(82−46, 82, 81)-Net over F₉ — Constructive and digital

Digital (36, 82, 81)-net over F₉, using

t-expansion [i] based on digital (32, 82, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(82−46, 82, 84)-Net in Base 9 — Constructive

(36, 82, 84)-net in base 9, using

2 times m-reduction [i] based on (36, 84, 84)-net in base 9, using
- base change [i] based on digital (8, 56, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(82−46, 82, 128)-Net over F₉ — Digital

Digital (36, 82, 128)-net over F₉, using

t-expansion [i] based on digital (33, 82, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(82−46, 82, 2960)-Net in Base 9 — Upper bound on s

There is no (36, 82, 2961)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 771295 453230 379407 318993 623659 991644 277988 099179 895234 761723 952901 655147 438969 > 9⁸² [i]