MinT - Best Known (65, 143, s)-Nets in Base 4

Best Known (65, 143, s)-Nets in Base 4

(65, 143, 66)-Net over F₄ — Constructive and digital

Digital (65, 143, 66)-net over F₄, using

t-expansion [i] based on digital (49, 143, 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]

(65, 143, 99)-Net over F₄ — Digital

Digital (65, 143, 99)-net over F₄, using

t-expansion [i] based on digital (61, 143, 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]

(65, 143, 796)-Net in Base 4 — Upper bound on s

There is no (65, 143, 797)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 129 502851 774512 337843 120195 945601 419402 433539 926472 206946 079238 508917 028966 621023 082688 > 4¹⁴³ [i]