MinT - Best Known (220−65, 220, s)-Nets in Base 3

Best Known (220−65, 220, s)-Nets in Base 3

(220−65, 220, 252)-Net over F₃ — Constructive and digital

Digital (155, 220, 252)-net over F₃, using

3¹ times duplication [i] based on digital (154, 219, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 73, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(220−65, 220, 506)-Net over F₃ — Digital

Digital (155, 220, 506)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−65, 220, 11748)-Net in Base 3 — Upper bound on s

There is no (155, 220, 11749)-net in base 3, because

1 times m-reduction [i] would yield (155, 219, 11749)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 309 019447 820916 926081 309060 463179 937967 289293 426460 320213 429082 237533 513643 113550 010441 591998 938630 150017 > 3²¹⁹ [i]