MinT - Best Known (101, 101+138, s)-Nets in Base 4

Best Known (101, 101+138, s)-Nets in Base 4

(101, 101+138, 104)-Net over F₄ — Constructive and digital

Digital (101, 239, 104)-net over F₄, using

t-expansion [i] based on digital (73, 239, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(101, 101+138, 144)-Net over F₄ — Digital

Digital (101, 239, 144)-net over F₄, using

t-expansion [i] based on digital (91, 239, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(101, 101+138, 1020)-Net in Base 4 — Upper bound on s

There is no (101, 239, 1021)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 808329 719894 377206 951180 518696 655643 677933 669024 347908 443679 431917 961452 522067 323322 305898 919438 775510 202216 515157 433566 781267 069187 618420 768596 > 4²³⁹ [i]