MinT - Best Known (179−121, 179, s)-Nets in Base 4

Best Known (179−121, 179, s)-Nets in Base 4

(179−121, 179, 66)-Net over F₄ — Constructive and digital

Digital (58, 179, 66)-net over F₄, using

t-expansion [i] based on digital (49, 179, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(179−121, 179, 91)-Net over F₄ — Digital

Digital (58, 179, 91)-net over F₄, using

t-expansion [i] based on digital (50, 179, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(179−121, 179, 424)-Net in Base 4 — Upper bound on s

There is no (58, 179, 425)-net in base 4, because

1 times m-reduction [i] would yield (58, 178, 425)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150628 234571 106371 721085 011281 078950 804539 550786 703499 186099 296764 282932 702637 613675 244041 495145 660956 506720 > 4¹⁷⁸ [i]