MinT - Best Known (185−73, 185, s)-Nets in Base 4

Best Known (185−73, 185, s)-Nets in Base 4

(185−73, 185, 130)-Net over F₄ — Constructive and digital

Digital (112, 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]

(185−73, 185, 286)-Net over F₄ — Digital

Digital (112, 185, 286)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−73, 185, 5656)-Net in Base 4 — Upper bound on s

There is no (112, 185, 5657)-net in base 4, because

1 times m-reduction [i] would yield (112, 184, 5657)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 602 685249 235634 838166 207237 168653 346293 377931 885711 743690 394286 640135 083905 777332 578597 429858 707800 700773 828320 > 4¹⁸⁴ [i]