MinT - Best Known (112, 112+93, s)-Nets in Base 4

Best Known (112, 112+93, s)-Nets in Base 4

(112, 112+93, 130)-Net over F₄ — Constructive and digital

Digital (112, 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]

(112, 112+93, 199)-Net over F₄ — Digital

Digital (112, 205, 199)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+93, 2768)-Net in Base 4 — Upper bound on s

There is no (112, 205, 2769)-net in base 4, because

1 times m-reduction [i] would yield (112, 204, 2769)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 666 181805 304597 061616 902514 054002 177616 902440 147270 482761 948409 532190 378163 169821 907988 715532 489406 289554 905817 206041 320048 > 4²⁰⁴ [i]