MinT - Best Known (121, 244, s)-Nets in Base 4

Best Known (121, 244, s)-Nets in Base 4

(121, 244, 130)-Net over F₄ — Constructive and digital

Digital (121, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(121, 244, 168)-Net over F₄ — Digital

Digital (121, 244, 168)-net over F₄, using

t-expansion [i] based on digital (115, 244, 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]

(121, 244, 1915)-Net in Base 4 — Upper bound on s

There is no (121, 244, 1916)-net in base 4, because

1 times m-reduction [i] would yield (121, 243, 1916)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 202 037034 014158 463253 732015 745500 349114 290405 349005 765762 319272 635547 619180 732293 314229 480945 406430 211156 777662 431435 664138 091850 342302 475562 904880 > 4²⁴³ [i]