MinT - Best Known (130, 130+111, s)-Nets in Base 4

Best Known (130, 130+111, s)-Nets in Base 4

(130, 130+111, 130)-Net over F₄ — Constructive and digital

Digital (130, 241, 130)-net over F₄, using

t-expansion [i] based on digital (105, 241, 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]

(130, 130+111, 220)-Net over F₄ — Digital

Digital (130, 241, 220)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+111, 2969)-Net in Base 4 — Upper bound on s

There is no (130, 241, 2970)-net in base 4, because

1 times m-reduction [i] would yield (130, 240, 2970)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 157787 525286 163722 486036 167756 039274 406506 813552 583684 883390 318358 852467 492814 322272 325962 242959 687814 472890 913182 950383 432673 213911 291750 969520 > 4²⁴⁰ [i]