MinT - Best Known (169−55, 169, s)-Nets in Base 4

Best Known (169−55, 169, s)-Nets in Base 4

(169−55, 169, 240)-Net over F₄ — Constructive and digital

Digital (114, 169, 240)-net over F₄, using

4¹ times duplication [i] based on digital (113, 168, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 56, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(169−55, 169, 521)-Net over F₄ — Digital

Digital (114, 169, 521)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−55, 169, 20275)-Net in Base 4 — Upper bound on s

There is no (114, 169, 20276)-net in base 4, because

1 times m-reduction [i] would yield (114, 168, 20276)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 140127 536501 541513 807941 344803 580577 756640 643996 925659 203192 800810 993274 876221 143661 213424 332130 230452 > 4¹⁶⁸ [i]