MinT - Best Known (18, 80, s)-Nets in Base 81

Best Known (18, 80, s)-Nets in Base 81

(18, 80, 370)-Net over F₈₁ — Constructive and digital

Digital (18, 80, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 80, 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]

(18, 80, 13048)-Net in Base 81 — Upper bound on s

There is no (18, 80, 13049)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 478 106739 228193 149216 551667 579749 250471 210600 049003 468160 836046 636747 335873 888753 638696 141539 490434 868559 680922 264008 570052 418230 900057 826676 328269 961521 > 81⁸⁰ [i]