MinT - Best Known (223−79, 223, s)-Nets in Base 3

Best Known (223−79, 223, s)-Nets in Base 3

(223−79, 223, 162)-Net over F₃ — Constructive and digital

Digital (144, 223, 162)-net over F₃, using

1 times m-reduction [i] based on digital (144, 224, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 112, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(223−79, 223, 291)-Net over F₃ — Digital

Digital (144, 223, 291)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−79, 223, 3964)-Net in Base 3 — Upper bound on s

There is no (144, 223, 3965)-net in base 3, because

1 times m-reduction [i] would yield (144, 222, 3965)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8415 648161 056305 721294 739432 917510 161382 617232 075044 264042 341153 454335 684733 541219 951778 950079 953773 679163 > 3²²² [i]