MinT - Best Known (199−83, 199, s)-Nets in Base 4

Best Known (199−83, 199, s)-Nets in Base 4

(199−83, 199, 130)-Net over F₄ — Constructive and digital

Digital (116, 199, 130)-net over F₄, using

t-expansion [i] based on digital (105, 199, 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]

(199−83, 199, 254)-Net over F₄ — Digital

Digital (116, 199, 254)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−83, 199, 4314)-Net in Base 4 — Upper bound on s

There is no (116, 199, 4315)-net in base 4, because

1 times m-reduction [i] would yield (116, 198, 4315)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 162082 466524 658817 931984 342196 063559 816299 778632 720972 062846 311347 334676 776469 277356 026404 862406 491245 081693 756340 002020 > 4¹⁹⁸ [i]