MinT - Best Known (66−42, 66, s)-Nets in Base 81

Best Known (66−42, 66, s)-Nets in Base 81

(66−42, 66, 370)-Net over F₈₁ — Constructive and digital

Digital (24, 66, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 66, 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]

(66−42, 66, 108008)-Net in Base 81 — Upper bound on s

There is no (24, 66, 108009)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 912160 292541 827037 578681 941703 187588 660613 028649 503602 311105 681021 355466 285537 115999 210928 947635 652103 026816 786648 927422 735121 > 81⁶⁶ [i]