MinT - Best Known (24, 24+34, s)-Nets in Base 81

Best Known (24, 24+34, s)-Nets in Base 81

(24, 24+34, 370)-Net over F₈₁ — Constructive and digital

Digital (24, 58, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 58, 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]

(24, 24+34, 388)-Net over F₈₁ — Digital

Digital (24, 58, 388)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(24, 24+34, 291168)-Net in Base 81 — Upper bound on s

There is no (24, 58, 291169)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 492 194541 120068 923043 339502 822332 011583 619959 754508 142766 921228 773088 729860 489303 324434 014602 263671 764502 485841 > 81⁵⁸ [i]