MinT - Best Known (220−53, 220, s)-Nets in Base 3

Best Known (220−53, 220, s)-Nets in Base 3

(220−53, 220, 464)-Net over F₃ — Constructive and digital

Digital (167, 220, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 55, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(220−53, 220, 1066)-Net over F₃ — Digital

Digital (167, 220, 1066)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−53, 220, 55066)-Net in Base 3 — Upper bound on s

There is no (167, 220, 55067)-net in base 3, because

1 times m-reduction [i] would yield (167, 219, 55067)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 308 719696 042309 058036 855452 461232 236559 995356 296568 570579 672336 637473 524116 120658 842761 595725 360968 419045 > 3²¹⁹ [i]