MinT - Best Known (169−112, 169, s)-Nets in Base 4

Best Known (169−112, 169, s)-Nets in Base 4

(169−112, 169, 66)-Net over F₄ — Constructive and digital

Digital (57, 169, 66)-net over F₄, using

t-expansion [i] based on digital (49, 169, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(169−112, 169, 91)-Net over F₄ — Digital

Digital (57, 169, 91)-net over F₄, using

t-expansion [i] based on digital (50, 169, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(169−112, 169, 430)-Net in Base 4 — Upper bound on s

There is no (57, 169, 431)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 615435 077941 750513 255709 654235 581002 154223 479093 592269 617172 590176 115519 909205 246516 878933 282074 234424 > 4¹⁶⁹ [i]