MinT - Best Known (119, 119+75, s)-Nets in Base 3

Best Known (119, 119+75, s)-Nets in Base 3

(119, 119+75, 156)-Net over F₃ — Constructive and digital

Digital (119, 194, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 97, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(119, 119+75, 201)-Net over F₃ — Digital

Digital (119, 194, 201)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+75, 2221)-Net in Base 3 — Upper bound on s

There is no (119, 194, 2222)-net in base 3, because

1 times m-reduction [i] would yield (119, 193, 2222)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 122 738011 718813 683388 609552 262578 426041 117274 486472 839950 188276 540024 217109 829679 947877 119669 > 3¹⁹³ [i]