MinT - Best Known (26, 26+41, s)-Nets in Base 81

Best Known (26, 26+41, s)-Nets in Base 81

(26, 26+41, 370)-Net over F₈₁ — Constructive and digital

Digital (26, 67, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 67, 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+41, 500)-Net over F₈₁ — Digital

Digital (26, 67, 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+41, 206156)-Net in Base 81 — Upper bound on s

There is no (26, 67, 206157)-net in base 81, because

1 times m-reduction [i] would yield (26, 66, 206157)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 912110 835192 527833 933382 528945 536525 414184 684282 503794 683936 049567 563600 325778 618999 113163 460087 634728 325478 884143 276767 419201 > 81⁶⁶ [i]