MinT - Best Known (18, 18+29, s)-Nets in Base 81

Best Known (18, 18+29, s)-Nets in Base 81

(18, 18+29, 370)-Net over F₈₁ — Constructive and digital

Digital (18, 47, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 47, 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, 18+29, 140956)-Net in Base 81 — Upper bound on s

There is no (18, 47, 140957)-net in base 81, because

1 times m-reduction [i] would yield (18, 46, 140957)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 6170 956032 542933 982175 413520 652655 862437 479435 234091 366598 681418 839119 936496 869321 091041 > 81⁴⁶ [i]