MinT - Best Known (227−111, 227, s)-Nets in Base 4

Best Known (227−111, 227, s)-Nets in Base 4

(227−111, 227, 130)-Net over F₄ — Constructive and digital

Digital (116, 227, 130)-net over F₄, using

t-expansion [i] based on digital (105, 227, 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]

(227−111, 227, 172)-Net over F₄ — Digital

Digital (116, 227, 172)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−111, 227, 2073)-Net in Base 4 — Upper bound on s

There is no (116, 227, 2074)-net in base 4, because

1 times m-reduction [i] would yield (116, 226, 2074)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11879 956578 342914 888094 454235 940167 048121 835476 845778 393686 820816 839036 893984 889972 963440 118059 445375 349352 154039 223881 106192 699865 746688 > 4²²⁶ [i]