MinT - Best Known (107, 107+115, s)-Nets in Base 4

Best Known (107, 107+115, s)-Nets in Base 4

(107, 107+115, 130)-Net over F₄ — Constructive and digital

Digital (107, 222, 130)-net over F₄, using

t-expansion [i] based on digital (105, 222, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(107, 107+115, 144)-Net over F₄ — Digital

Digital (107, 222, 144)-net over F₄, using

t-expansion [i] based on digital (91, 222, 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]

(107, 107+115, 1542)-Net in Base 4 — Upper bound on s

There is no (107, 222, 1543)-net in base 4, because

1 times m-reduction [i] would yield (107, 221, 1543)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 472523 971682 489970 870406 616724 655687 187414 495762 697921 576886 170254 801963 858188 223872 605163 004940 011895 020110 009590 961484 152722 515840 > 4²²¹ [i]