MinT - Best Known (116−64, 116, s)-Nets in Base 4

Best Known (116−64, 116, s)-Nets in Base 4

(116−64, 116, 66)-Net over F₄ — Constructive and digital

Digital (52, 116, 66)-net over F₄, using

t-expansion [i] based on digital (49, 116, 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]

(116−64, 116, 91)-Net over F₄ — Digital

Digital (52, 116, 91)-net over F₄, using

t-expansion [i] based on digital (50, 116, 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]

(116−64, 116, 623)-Net in Base 4 — Upper bound on s

There is no (52, 116, 624)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7178 296676 278859 530013 393713 445974 901089 048069 842783 166606 570329 872155 > 4¹¹⁶ [i]