MinT - Best Known (56, 146, s)-Nets in Base 4

Best Known (56, 146, s)-Nets in Base 4

(56, 146, 66)-Net over F₄ — Constructive and digital

Digital (56, 146, 66)-net over F₄, using

t-expansion [i] based on digital (49, 146, 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]

(56, 146, 91)-Net over F₄ — Digital

Digital (56, 146, 91)-net over F₄, using

t-expansion [i] based on digital (50, 146, 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]

(56, 146, 491)-Net in Base 4 — Upper bound on s

There is no (56, 146, 492)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8179 742413 573528 564853 647460 156172 352918 073340 618524 831344 533298 418029 747410 663873 418384 > 4¹⁴⁶ [i]