MinT - Best Known (185−71, 185, s)-Nets in Base 4

Best Known (185−71, 185, s)-Nets in Base 4

(185−71, 185, 130)-Net over F₄ — Constructive and digital

Digital (114, 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]

(185−71, 185, 314)-Net over F₄ — Digital

Digital (114, 185, 314)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−71, 185, 6751)-Net in Base 4 — Upper bound on s

There is no (114, 185, 6752)-net in base 4, because

1 times m-reduction [i] would yield (114, 184, 6752)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 601 784570 087856 657366 000792 848857 206262 257662 817952 744992 721368 863158 761374 195402 416054 444024 937588 878962 627514 > 4¹⁸⁴ [i]