MinT - Best Known (52, 100, s)-Nets in Base 4

Best Known (52, 100, s)-Nets in Base 4

(52, 100, 66)-Net over F₄ — Constructive and digital

Digital (52, 100, 66)-net over F₄, using

t-expansion [i] based on digital (49, 100, 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]

(52, 100, 91)-Net over F₄ — Digital

Digital (52, 100, 91)-net over F₄, using

t-expansion [i] based on digital (50, 100, 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]

(52, 100, 1034)-Net in Base 4 — Upper bound on s

There is no (52, 100, 1035)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 621664 120961 821020 348483 464247 842219 677572 124332 101416 889664 > 4¹⁰⁰ [i]