MinT - Best Known (117, 249, s)-Nets in Base 4

Best Known (117, 249, s)-Nets in Base 4

(117, 249, 130)-Net over F₄ — Constructive and digital

Digital (117, 249, 130)-net over F₄, using

t-expansion [i] based on digital (105, 249, 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, 249, 168)-Net over F₄ — Digital

Digital (117, 249, 168)-net over F₄, using

t-expansion [i] based on digital (115, 249, 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, 249, 1528)-Net in Base 4 — Upper bound on s

There is no (117, 249, 1529)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 824475 014774 087758 424315 430444 756389 718952 146831 627196 024955 611923 409719 344924 497335 221564 647470 207599 194170 709658 121340 039024 783519 272236 047407 519700 > 4²⁴⁹ [i]