MinT - Best Known (101, 101+126, s)-Nets in Base 4

Best Known (101, 101+126, s)-Nets in Base 4

(101, 101+126, 104)-Net over F₄ — Constructive and digital

Digital (101, 227, 104)-net over F₄, using

t-expansion [i] based on digital (73, 227, 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+126, 144)-Net over F₄ — Digital

Digital (101, 227, 144)-net over F₄, using

t-expansion [i] based on digital (91, 227, 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+126, 1145)-Net in Base 4 — Upper bound on s

There is no (101, 227, 1146)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48407 386172 579633 706860 156037 569380 884266 598958 643465 441754 369465 090427 035406 780782 245213 063117 353842 057123 193945 777556 697204 849965 046304 > 4²²⁷ [i]