MinT - Best Known (185−77, 185, s)-Nets in Base 4

Best Known (185−77, 185, s)-Nets in Base 4

(185−77, 185, 130)-Net over F₄ — Constructive and digital

Digital (108, 185, 130)-net over F₄, using

t-expansion [i] based on digital (105, 185, 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]

(185−77, 185, 240)-Net over F₄ — Digital

Digital (108, 185, 240)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−77, 185, 4089)-Net in Base 4 — Upper bound on s

There is no (108, 185, 4090)-net in base 4, because

1 times m-reduction [i] would yield (108, 184, 4090)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 606 029018 486453 506292 998344 179324 923869 282059 194686 948481 912213 692707 095849 715269 815415 824921 420437 746754 497084 > 4¹⁸⁴ [i]