MinT - Best Known (229−109, 229, s)-Nets in Base 4

Best Known (229−109, 229, s)-Nets in Base 4

(229−109, 229, 130)-Net over F₄ — Constructive and digital

Digital (120, 229, 130)-net over F₄, using

t-expansion [i] based on digital (105, 229, 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]

(229−109, 229, 189)-Net over F₄ — Digital

Digital (120, 229, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−109, 229, 2390)-Net in Base 4 — Upper bound on s

There is no (120, 229, 2391)-net in base 4, because

1 times m-reduction [i] would yield (120, 228, 2391)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 187941 620485 782749 027883 464688 465677 457480 499402 967358 840954 249215 801465 952526 275981 628863 545995 189865 731213 016038 513487 382846 629109 365146 > 4²²⁸ [i]