MinT - Best Known (126, 126+97, s)-Nets in Base 3

Best Known (126, 126+97, s)-Nets in Base 3

(126, 126+97, 128)-Net over F₃ — Constructive and digital

Digital (126, 223, 128)-net over F₃, using

3 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, 126+97, 162)-Net over F₃ — Digital

Digital (126, 223, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+97, 1461)-Net in Base 3 — Upper bound on s

There is no (126, 223, 1462)-net in base 3, because

1 times m-reduction [i] would yield (126, 222, 1462)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8531 990123 727703 478145 882901 494150 248429 754909 797665 102355 312168 092040 525968 052554 280332 239506 756337 628641 > 3²²² [i]