MinT - Best Known (131, 242, s)-Nets in Base 4

Best Known (131, 242, s)-Nets in Base 4

(131, 242, 130)-Net over F₄ — Constructive and digital

Digital (131, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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]

(131, 242, 223)-Net over F₄ — Digital

Digital (131, 242, 223)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 242, 3046)-Net in Base 4 — Upper bound on s

There is no (131, 242, 3047)-net in base 4, because

1 times m-reduction [i] would yield (131, 241, 3047)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 641156 194255 573070 015289 765152 555600 327691 568945 388008 413223 670775 616493 804681 220420 955423 148784 426063 842288 577164 371651 203826 007180 164595 168560 > 4²⁴¹ [i]