MinT - Best Known (173−67, 173, s)-Nets in Base 4

Best Known (173−67, 173, s)-Nets in Base 4

(173−67, 173, 130)-Net over F₄ — Constructive and digital

Digital (106, 173, 130)-net over F₄, using

t-expansion [i] based on digital (105, 173, 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]

(173−67, 173, 287)-Net over F₄ — Digital

Digital (106, 173, 287)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−67, 173, 6002)-Net in Base 4 — Upper bound on s

There is no (106, 173, 6003)-net in base 4, because

1 times m-reduction [i] would yield (106, 172, 6003)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36 031050 030154 392623 357517 471707 650604 812134 048693 645586 365615 484926 125301 646878 014081 795100 350368 465690 > 4¹⁷² [i]