MinT - Best Known (124, 239, s)-Nets in Base 4

Best Known (124, 239, s)-Nets in Base 4

(124, 239, 130)-Net over F₄ — Constructive and digital

Digital (124, 239, 130)-net over F₄, using

t-expansion [i] based on digital (105, 239, 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]

(124, 239, 190)-Net over F₄ — Digital

Digital (124, 239, 190)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(124, 239, 2356)-Net in Base 4 — Upper bound on s

There is no (124, 239, 2357)-net in base 4, because

1 times m-reduction [i] would yield (124, 238, 2357)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 198541 550999 590983 854221 007294 410623 581228 374829 419910 848421 506263 809402 049147 767867 600766 092725 692074 664105 790811 688926 782374 303640 143677 758720 > 4²³⁸ [i]