MinT - Best Known (28, 28+32, s)-Nets in Base 81

Best Known (28, 28+32, s)-Nets in Base 81

(28, 28+32, 370)-Net over F₈₁ — Constructive and digital

Digital (28, 60, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 60, 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]

(28, 28+32, 783)-Net over F₈₁ — Digital

Digital (28, 60, 783)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(28, 28+32, 1219733)-Net in Base 81 — Upper bound on s

There is no (28, 60, 1219734)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 3 229283 270582 347911 344857 571753 625510 424307 756211 677725 324532 086133 604320 785124 954507 508892 152376 879318 939503 019521 > 81⁶⁰ [i]