MinT - Best Known (234−116, 234, s)-Nets in Base 4

Best Known (234−116, 234, s)-Nets in Base 4

(234−116, 234, 130)-Net over F₄ — Constructive and digital

Digital (118, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(234−116, 234, 170)-Net over F₄ — Digital

Digital (118, 234, 170)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−116, 234, 1962)-Net in Base 4 — Upper bound on s

There is no (118, 234, 1963)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 780 353708 943563 210899 839779 046094 101165 738184 504185 796286 053601 946736 961999 467079 220145 678024 230076 527570 414820 670329 561746 716789 035048 253800 > 4²³⁴ [i]