MinT - Best Known (117, 117+115, s)-Nets in Base 4

Best Known (117, 117+115, s)-Nets in Base 4

(117, 117+115, 130)-Net over F₄ — Constructive and digital

Digital (117, 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]

(117, 117+115, 168)-Net over F₄ — Digital

Digital (117, 232, 168)-net over F₄, using

t-expansion [i] based on digital (115, 232, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(117, 117+115, 1980)-Net in Base 4 — Upper bound on s

There is no (117, 232, 1981)-net in base 4, because

1 times m-reduction [i] would yield (117, 231, 1981)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 190414 864162 647060 660255 584928 870390 674104 979188 570161 727840 229687 291366 813812 666232 376509 596211 687629 517139 498925 260220 860923 173083 762352 > 4²³¹ [i]