MinT - Best Known (197−81, 197, s)-Nets in Base 4

Best Known (197−81, 197, s)-Nets in Base 4

(197−81, 197, 130)-Net over F₄ — Constructive and digital

Digital (116, 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]

(197−81, 197, 264)-Net over F₄ — Digital

Digital (116, 197, 264)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−81, 197, 4652)-Net in Base 4 — Upper bound on s

There is no (116, 197, 4653)-net in base 4, because

1 times m-reduction [i] would yield (116, 196, 4653)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10100 732107 620623 143992 220915 601465 941034 609053 727767 245889 233444 622847 161034 772640 189764 757288 339592 882175 676707 856183 > 4¹⁹⁶ [i]