MinT - Best Known (108, 108+125, s)-Nets in Base 4

Best Known (108, 108+125, s)-Nets in Base 4

(108, 108+125, 130)-Net over F₄ — Constructive and digital

Digital (108, 233, 130)-net over F₄, using

t-expansion [i] based on digital (105, 233, 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]

(108, 108+125, 144)-Net over F₄ — Digital

Digital (108, 233, 144)-net over F₄, using

t-expansion [i] based on digital (91, 233, 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]

(108, 108+125, 1377)-Net in Base 4 — Upper bound on s

There is no (108, 233, 1378)-net in base 4, because

1 times m-reduction [i] would yield (108, 232, 1378)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48 507632 623367 166168 041962 230673 746759 925800 128524 064072 440649 271748 846891 820913 853532 590179 112291 368904 780605 956443 889483 560663 806069 855328 > 4²³² [i]