MinT - Best Known (232−125, 232, s)-Nets in Base 4

Best Known (232−125, 232, s)-Nets in Base 4

(232−125, 232, 130)-Net over F₄ — Constructive and digital

Digital (107, 232, 130)-net over F₄, using

t-expansion [i] based on digital (105, 232, 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]

(232−125, 232, 144)-Net over F₄ — Digital

Digital (107, 232, 144)-net over F₄, using

t-expansion [i] based on digital (91, 232, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(232−125, 232, 1346)-Net in Base 4 — Upper bound on s

There is no (107, 232, 1347)-net in base 4, because

1 times m-reduction [i] would yield (107, 231, 1347)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 438004 607227 765490 343209 077201 180687 089805 193087 028773 895387 211126 831138 810033 675509 760690 329421 596963 905975 797180 071085 435890 155191 603600 > 4²³¹ [i]