MinT - Best Known (26, 26+51, s)-Nets in Base 81

Best Known (26, 26+51, s)-Nets in Base 81

(26, 26+51, 370)-Net over F₈₁ — Constructive and digital

Digital (26, 77, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 77, 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]

(26, 26+51, 500)-Net over F₈₁ — Digital

Digital (26, 77, 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]

(26, 26+51, 80586)-Net in Base 81 — Upper bound on s

There is no (26, 77, 80587)-net in base 81, because

1 times m-reduction [i] would yield (26, 76, 80587)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 11 088872 245768 576054 878927 723030 436276 305760 256805 535054 788748 016901 573102 567476 963275 978610 804007 250880 126098 720430 004598 341986 920576 105309 334001 > 81⁷⁶ [i]