MinT - Best Known (88, 88+60, s)-Nets in Base 3

Best Known (88, 88+60, s)-Nets in Base 3

(88, 88+60, 128)-Net over F₃ — Constructive and digital

Digital (88, 148, 128)-net over F₃, using

2 times m-reduction [i] based on digital (88, 150, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 75, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(88, 88+60, 139)-Net over F₃ — Digital

Digital (88, 148, 139)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+60, 1330)-Net in Base 3 — Upper bound on s

There is no (88, 148, 1331)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41273 013651 327612 406477 621063 526167 131075 052303 162678 623782 728214 799245 > 3¹⁴⁸ [i]