MinT - Best Known (229−113, 229, s)-Nets in Base 4

Best Known (229−113, 229, s)-Nets in Base 4

(229−113, 229, 130)-Net over F₄ — Constructive and digital

Digital (116, 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]

(229−113, 229, 169)-Net over F₄ — Digital

Digital (116, 229, 169)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−113, 229, 1999)-Net in Base 4 — Upper bound on s

There is no (116, 229, 2000)-net in base 4, because

1 times m-reduction [i] would yield (116, 228, 2000)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 188338 422732 550694 794033 320799 378779 340147 824266 364609 198577 961956 319964 518309 018655 775908 826566 788726 343818 696680 699551 076545 093515 183716 > 4²²⁸ [i]