MinT - Best Known (233−79, 233, s)-Nets in Base 3

Best Known (233−79, 233, s)-Nets in Base 3

(233−79, 233, 162)-Net over F₃ — Constructive and digital

Digital (154, 233, 162)-net over F₃, using

11 times m-reduction [i] based on digital (154, 244, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 122, 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]

(233−79, 233, 345)-Net over F₃ — Digital

Digital (154, 233, 345)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(233−79, 233, 5266)-Net in Base 3 — Upper bound on s

There is no (154, 233, 5267)-net in base 3, because

1 times m-reduction [i] would yield (154, 232, 5267)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 494 925926 997100 967048 487244 598698 200614 497926 113622 656466 336965 533169 120294 104628 221900 442718 088677 384409 592067 > 3²³² [i]