MinT - Best Known (19, 19+54, s)-Nets in Base 81

Best Known (19, 19+54, s)-Nets in Base 81

(19, 19+54, 370)-Net over F₈₁ — Constructive and digital

Digital (19, 73, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 73, 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]

(19, 19+54, 19724)-Net in Base 81 — Upper bound on s

There is no (19, 73, 19725)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 20 884843 089875 562164 951003 154663 419967 251807 272508 042524 922846 305029 858033 757704 929351 195662 300768 763207 723062 855764 812925 955063 462339 726001 > 81⁷³ [i]