MinT - Best Known (194−89, 194, s)-Nets in Base 4

Best Known (194−89, 194, s)-Nets in Base 4

(194−89, 194, 130)-Net over F₄ — Constructive and digital

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]

(194−89, 194, 183)-Net over F₄ — Digital

Digital (105, 194, 183)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−89, 194, 2479)-Net in Base 4 — Upper bound on s

There is no (105, 194, 2480)-net in base 4, because

1 times m-reduction [i] would yield (105, 193, 2480)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 158 404945 056459 953638 111847 470638 495032 551821 493875 985878 761971 480161 093577 285565 205123 529730 654072 396110 917287 962819 > 4¹⁹³ [i]