MinT - Best Known (210−97, 210, s)-Nets in Base 4

Best Known (210−97, 210, s)-Nets in Base 4

(210−97, 210, 130)-Net over F₄ — Constructive and digital

Digital (113, 210, 130)-net over F₄, using

t-expansion [i] based on digital (105, 210, 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]

(210−97, 210, 192)-Net over F₄ — Digital

Digital (113, 210, 192)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−97, 210, 2573)-Net in Base 4 — Upper bound on s

There is no (113, 210, 2574)-net in base 4, because

1 times m-reduction [i] would yield (113, 209, 2574)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 680429 677721 524684 307955 073928 984875 062509 775258 303441 602735 565401 758487 231526 332110 935538 300924 297848 050613 219850 516027 124320 > 4²⁰⁹ [i]