MinT - Best Known (131, 131+127, s)-Nets in Base 4

Best Known (131, 131+127, s)-Nets in Base 4

(131, 131+127, 130)-Net over F₄ — Constructive and digital

Digital (131, 258, 130)-net over F₄, using

t-expansion [i] based on digital (105, 258, 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+127, 189)-Net over F₄ — Digital

Digital (131, 258, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+127, 2263)-Net in Base 4 — Upper bound on s

There is no (131, 258, 2264)-net in base 4, because

1 times m-reduction [i] would yield (131, 257, 2264)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 54290 280911 848363 830352 708465 741639 143693 033983 652672 455239 265531 481574 626282 686540 721238 523373 167165 015910 022839 700201 167060 495461 795378 185165 409294 721016 > 4²⁵⁷ [i]