MinT - Best Known (173−55, 173, s)-Nets in Base 4

Best Known (173−55, 173, s)-Nets in Base 4

(173−55, 173, 240)-Net over F₄ — Constructive and digital

Digital (118, 173, 240)-net over F₄, using

t-expansion [i] based on digital (117, 173, 240)-net over F₄, using
- 1 times m-reduction [i] based on digital (117, 174, 240)-net over F₄, using
  - trace code for nets [i] based on digital (1, 58, 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]

(173−55, 173, 581)-Net over F₄ — Digital

Digital (118, 173, 581)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−55, 173, 24902)-Net in Base 4 — Upper bound on s

There is no (118, 173, 24903)-net in base 4, because

1 times m-reduction [i] would yield (118, 172, 24903)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 845701 149450 236405 405949 633513 572436 916678 156164 100935 875318 507870 906508 924422 610526 771909 263305 429696 > 4¹⁷² [i]