MinT - Best Known (219−95, 219, s)-Nets in Base 4

Best Known (219−95, 219, s)-Nets in Base 4

(219−95, 219, 130)-Net over F₄ — Constructive and digital

Digital (124, 219, 130)-net over F₄, using

t-expansion [i] based on digital (105, 219, 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]

(219−95, 219, 244)-Net over F₄ — Digital

Digital (124, 219, 244)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(219−95, 219, 3759)-Net in Base 4 — Upper bound on s

There is no (124, 219, 3760)-net in base 4, because

1 times m-reduction [i] would yield (124, 218, 3760)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 179428 647657 665719 599330 143632 728082 449450 855843 050933 311635 571499 769731 509211 809769 249312 863872 364676 596260 027167 386498 920908 479411 > 4²¹⁸ [i]