MinT - Best Known (126, 221, s)-Nets in Base 3

Best Known (126, 221, s)-Nets in Base 3

(126, 221, 128)-Net over F₃ — Constructive and digital

Digital (126, 221, 128)-net over F₃, using

5 times m-reduction [i] based on digital (126, 226, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 113, 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]

(126, 221, 167)-Net over F₃ — Digital

Digital (126, 221, 167)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 221, 1525)-Net in Base 3 — Upper bound on s

There is no (126, 221, 1526)-net in base 3, because

1 times m-reduction [i] would yield (126, 220, 1526)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 929 332696 809257 802329 457513 547226 423458 420318 687397 718324 373311 834828 419593 484464 950630 952202 269373 355465 > 3²²⁰ [i]