MinT - Best Known (88, 88+44, s)-Nets in Base 3

Best Known (88, 88+44, s)-Nets in Base 3

(88, 88+44, 156)-Net over F₃ — Constructive and digital

Digital (88, 132, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 66, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(88, 88+44, 225)-Net over F₃ — Digital

Digital (88, 132, 225)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+44, 3278)-Net in Base 3 — Upper bound on s

There is no (88, 132, 3279)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 956 045419 641319 644142 753709 227661 983112 329635 201507 385075 167477 > 3¹³² [i]