MinT - Best Known (220−101, 220, s)-Nets in Base 4

Best Known (220−101, 220, s)-Nets in Base 4

(220−101, 220, 130)-Net over F₄ — Constructive and digital

Digital (119, 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]

(220−101, 220, 204)-Net over F₄ — Digital

Digital (119, 220, 204)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−101, 220, 2774)-Net in Base 4 — Upper bound on s

There is no (119, 220, 2775)-net in base 4, because

1 times m-reduction [i] would yield (119, 219, 2775)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 714732 375617 620024 603153 874702 709772 069010 331396 491805 778332 169809 861779 924465 867618 086799 080787 116830 651331 971220 368189 630764 209906 > 4²¹⁹ [i]