MinT - Best Known (259−121, 259, s)-Nets in Base 4

Best Known (259−121, 259, s)-Nets in Base 4

(259−121, 259, 130)-Net over F₄ — Constructive and digital

Digital (138, 259, 130)-net over F₄, using

t-expansion [i] based on digital (105, 259, 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]

(259−121, 259, 224)-Net over F₄ — Digital

Digital (138, 259, 224)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−121, 259, 2950)-Net in Base 4 — Upper bound on s

There is no (138, 259, 2951)-net in base 4, because

1 times m-reduction [i] would yield (138, 258, 2951)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 216785 909870 810634 976295 749545 414518 021820 000446 298531 721558 096240 501710 239215 013820 034476 707889 559206 350019 020795 544711 839638 730668 649884 239781 747236 838960 > 4²⁵⁸ [i]