MinT - Best Known (119, 119+83, s)-Nets in Base 4

Best Known (119, 119+83, s)-Nets in Base 4

(119, 119+83, 130)-Net over F₄ — Constructive and digital

Digital (119, 202, 130)-net over F₄, using

t-expansion [i] based on digital (105, 202, 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]

(119, 119+83, 270)-Net over F₄ — Digital

Digital (119, 202, 270)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+83, 4778)-Net in Base 4 — Upper bound on s

There is no (119, 202, 4779)-net in base 4, because

1 times m-reduction [i] would yield (119, 201, 4779)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 352062 071615 840887 131766 665504 569555 395332 512948 614126 712426 478081 853871 173904 816330 016934 262016 688427 061169 425060 465834 > 4²⁰¹ [i]