MinT - Best Known (112, 197, s)-Nets in Base 4

Best Known (112, 197, s)-Nets in Base 4

(112, 197, 130)-Net over F₄ — Constructive and digital

Digital (112, 197, 130)-net over F₄, using

t-expansion [i] based on digital (105, 197, 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, 197, 226)-Net over F₄ — Digital

Digital (112, 197, 226)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 197, 3516)-Net in Base 4 — Upper bound on s

There is no (112, 197, 3517)-net in base 4, because

1 times m-reduction [i] would yield (112, 196, 3517)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10187 195878 230154 824455 141570 344150 102655 292309 234190 886495 007649 384902 344043 475475 586615 441607 530141 638264 105540 119810 > 4¹⁹⁶ [i]