MinT - Best Known (131, 131+125, s)-Nets in Base 4

Best Known (131, 131+125, s)-Nets in Base 4

(131, 131+125, 130)-Net over F₄ — Constructive and digital

Digital (131, 256, 130)-net over F₄, using

t-expansion [i] based on digital (105, 256, 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, 131+125, 193)-Net over F₄ — Digital

Digital (131, 256, 193)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+125, 2337)-Net in Base 4 — Upper bound on s

There is no (131, 256, 2338)-net in base 4, because

1 times m-reduction [i] would yield (131, 255, 2338)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3390 269655 227956 943059 446439 201301 753647 989211 088340 910629 421971 265524 798770 111354 564736 349345 944647 842176 230279 665812 226436 932509 237480 337059 072556 032640 > 4²⁵⁵ [i]