MinT - Best Known (126, 219, s)-Nets in Base 3

Best Known (126, 219, s)-Nets in Base 3

(126, 219, 128)-Net over F₃ — Constructive and digital

Digital (126, 219, 128)-net over F₃, using

7 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, 219, 171)-Net over F₃ — Digital

Digital (126, 219, 171)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 219, 1596)-Net in Base 3 — Upper bound on s

There is no (126, 219, 1597)-net in base 3, because

1 times m-reduction [i] would yield (126, 218, 1597)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 103 217584 073414 834127 987786 779601 836429 043804 314524 837327 452709 537486 041955 883787 683535 248374 144264 083345 > 3²¹⁸ [i]