MinT - Best Known (173, 173+87, s)-Nets in Base 4

Best Known (173, 173+87, s)-Nets in Base 4

(173, 173+87, 450)-Net over F₄ — Constructive and digital

Digital (173, 260, 450)-net over F₄, using

t-expansion [i] based on digital (170, 260, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 130, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(173, 173+87, 684)-Net over F₄ — Digital

Digital (173, 260, 684)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173, 173+87, 23771)-Net in Base 4 — Upper bound on s

There is no (173, 260, 23772)-net in base 4, because

1 times m-reduction [i] would yield (173, 259, 23772)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 858250 172492 701425 817107 916328 422196 548313 515856 238488 245154 467999 289785 142039 814722 398898 507920 381754 086823 175091 761681 233185 876928 438987 928354 686392 563262 > 4²⁵⁹ [i]