MinT - Best Known (69−42, 69, s)-Nets in Base 81

Best Known (69−42, 69, s)-Nets in Base 81

(69−42, 69, 370)-Net over F₈₁ — Constructive and digital

Digital (27, 69, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 69, 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]

(69−42, 69, 500)-Net over F₈₁ — Digital

Digital (27, 69, 500)-net over F₈₁, using

t-expansion [i] based on digital (26, 69, 500)-net over F₈₁, using
- net from sequence [i] based on digital (26, 499)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 26 and N(F) ≥ 500, using
    - a curve from the manYPoints database [i]

(69−42, 69, 202356)-Net in Base 81 — Upper bound on s

There is no (27, 69, 202357)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 484720 295797 957039 263246 878386 080112 883708 812738 806456 417846 549177 770100 165642 718158 432479 502738 903290 075981 579485 994362 898664 631761 > 81⁶⁹ [i]