MinT - Best Known (206−138, 206, s)-Nets in Base 4

Best Known (206−138, 206, s)-Nets in Base 4

(206−138, 206, 66)-Net over F₄ — Constructive and digital

Digital (68, 206, 66)-net over F₄, using

t-expansion [i] based on digital (49, 206, 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]

(206−138, 206, 99)-Net over F₄ — Digital

Digital (68, 206, 99)-net over F₄, using

t-expansion [i] based on digital (61, 206, 99)-net over F₄, using
- net from sequence [i] based on digital (61, 98)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
    - Drinfeld modules of rank 1 [i]

(206−138, 206, 499)-Net in Base 4 — Upper bound on s

There is no (68, 206, 500)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10906 945785 100414 934707 850718 378533 407596 053828 663894 724254 769251 344913 281243 622453 523262 899546 928901 628188 536612 163004 727036 > 4²⁰⁶ [i]