MinT - Best Known (31, 31+42, s)-Nets in Base 81

Best Known (31, 31+42, s)-Nets in Base 81

(31, 31+42, 370)-Net over F₈₁ — Constructive and digital

Digital (31, 73, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 73, 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]

(31, 31+42, 551)-Net over F₈₁ — Digital

Digital (31, 73, 551)-net over F₈₁, using

t-expansion [i] based on digital (30, 73, 551)-net over F₈₁, using
- net from sequence [i] based on digital (30, 550)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 30 and N(F) ≥ 551, using
    - a curve from the manYPoints database [i]

(31, 31+42, 467358)-Net in Base 81 — Upper bound on s

There is no (31, 73, 467359)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 20 864543 906890 467691 043246 238140 799228 135326 631161 895090 469899 014050 188084 818435 588860 073239 406474 064249 087956 743414 214730 745764 073535 243121 > 81⁷³ [i]