MinT - Best Known (220−105, 220, s)-Nets in Base 4

Best Known (220−105, 220, s)-Nets in Base 4

(220−105, 220, 130)-Net over F₄ — Constructive and digital

Digital (115, 220, 130)-net over F₄, using

t-expansion [i] based on digital (105, 220, 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]

(220−105, 220, 181)-Net over F₄ — Digital

Digital (115, 220, 181)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−105, 220, 2271)-Net in Base 4 — Upper bound on s

There is no (115, 220, 2272)-net in base 4, because

1 times m-reduction [i] would yield (115, 219, 2272)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 717386 145353 167454 020726 400309 928974 342072 451533 874064 646581 870844 741292 910948 289870 344142 880295 956656 939319 334435 951205 970597 020410 > 4²¹⁹ [i]