MinT - Best Known (184−77, 184, s)-Nets in Base 4

Best Known (184−77, 184, s)-Nets in Base 4

(184−77, 184, 130)-Net over F₄ — Constructive and digital

Digital (107, 184, 130)-net over F₄, using

t-expansion [i] based on digital (105, 184, 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]

(184−77, 184, 235)-Net over F₄ — Digital

Digital (107, 184, 235)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−77, 184, 3941)-Net in Base 4 — Upper bound on s

There is no (107, 184, 3942)-net in base 4, because

1 times m-reduction [i] would yield (107, 183, 3942)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 972239 315334 314583 162958 487018 804672 516009 353830 982229 375173 491566 821112 576432 187495 249078 869171 689334 616040 > 4¹⁸³ [i]