MinT - Best Known (116, 116+89, s)-Nets in Base 4

Best Known (116, 116+89, s)-Nets in Base 4

(116, 116+89, 130)-Net over F₄ — Constructive and digital

Digital (116, 205, 130)-net over F₄, using

t-expansion [i] based on digital (105, 205, 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]

(116, 116+89, 229)-Net over F₄ — Digital

Digital (116, 205, 229)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+89, 3521)-Net in Base 4 — Upper bound on s

There is no (116, 205, 3522)-net in base 4, because

1 times m-reduction [i] would yield (116, 204, 3522)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 663 651803 414820 567988 742780 067121 369558 152516 577767 384303 806157 804702 990395 614243 400229 646555 038873 254289 306797 419839 530896 > 4²⁰⁴ [i]