MinT - Best Known (194−80, 194, s)-Nets in Base 4

Best Known (194−80, 194, s)-Nets in Base 4

(194−80, 194, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(194−80, 194, 258)-Net over F₄ — Digital

Digital (114, 194, 258)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−80, 194, 4339)-Net in Base 4 — Upper bound on s

There is no (114, 194, 4340)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 635 840438 343604 279343 323361 562421 134959 407617 714025 684332 749144 844159 791464 247272 842100 531401 426795 649826 939115 220390 > 4¹⁹⁴ [i]