MinT - Best Known (181−69, 181, s)-Nets in Base 4

Best Known (181−69, 181, s)-Nets in Base 4

(181−69, 181, 130)-Net over F₄ — Constructive and digital

Digital (112, 181, 130)-net over F₄, using

t-expansion [i] based on digital (105, 181, 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]

(181−69, 181, 315)-Net over F₄ — Digital

Digital (112, 181, 315)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(181−69, 181, 6918)-Net in Base 4 — Upper bound on s

There is no (112, 181, 6919)-net in base 4, because

1 times m-reduction [i] would yield (112, 180, 6919)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 358419 940283 851526 663883 932330 151522 746733 874581 571632 615770 137877 090930 476023 653946 643888 159301 119986 751064 > 4¹⁸⁰ [i]