MinT - Best Known (126, 126+92, s)-Nets in Base 3

Best Known (126, 126+92, s)-Nets in Base 3

(126, 126+92, 148)-Net over F₃ — Constructive and digital

Digital (126, 218, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 109, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(126, 126+92, 174)-Net over F₃ — Digital

Digital (126, 218, 174)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+92, 1596)-Net in Base 3 — Upper bound on s

There is no (126, 218, 1597)-net in base 3, because

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]