MinT - Best Known (108, 108+143, s)-Nets in Base 4

Best Known (108, 108+143, s)-Nets in Base 4

(108, 108+143, 130)-Net over F₄ — Constructive and digital

Digital (108, 251, 130)-net over F₄, using

t-expansion [i] based on digital (105, 251, 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+143, 144)-Net over F₄ — Digital

Digital (108, 251, 144)-net over F₄, using

t-expansion [i] based on digital (91, 251, 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+143, 1140)-Net in Base 4 — Upper bound on s

There is no (108, 251, 1141)-net in base 4, because

1 times m-reduction [i] would yield (108, 250, 1141)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 402293 236048 582801 767198 923321 401930 166775 019253 295336 498001 292860 789828 049171 514653 754141 764806 860300 993926 519834 930271 642671 013986 493414 240883 691536 > 4²⁵⁰ [i]