MinT - Best Known (194−78, 194, s)-Nets in Base 4

Best Known (194−78, 194, s)-Nets in Base 4

(194−78, 194, 130)-Net over F₄ — Constructive and digital

Digital (116, 194, 130)-net over F₄, using

t-expansion [i] based on digital (105, 194, 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]

(194−78, 194, 280)-Net over F₄ — Digital

Digital (116, 194, 280)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−78, 194, 5039)-Net in Base 4 — Upper bound on s

There is no (116, 194, 5040)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 630 778297 880013 540823 327066 021641 688815 505983 944994 199153 299996 746471 273341 765594 626823 116304 782889 376115 695498 395741 > 4¹⁹⁴ [i]