MinT - Best Known (185−75, 185, s)-Nets in Base 4

Best Known (185−75, 185, s)-Nets in Base 4

(185−75, 185, 130)-Net over F₄ — Constructive and digital

Digital (110, 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]

(185−75, 185, 261)-Net over F₄ — Digital

Digital (110, 185, 261)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−75, 185, 4787)-Net in Base 4 — Upper bound on s

There is no (110, 185, 4788)-net in base 4, because

1 times m-reduction [i] would yield (110, 184, 4788)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 604 907780 928606 975530 265343 031759 471513 722247 792207 449847 731671 991476 168215 049632 594646 728779 848308 175181 850908 > 4¹⁸⁴ [i]