MinT - Best Known (259−130, 259, s)-Nets in Base 4

Best Known (259−130, 259, s)-Nets in Base 4

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

Digital (129, 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]

(259−130, 259, 179)-Net over F₄ — Digital

Digital (129, 259, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(259−130, 259, 2038)-Net in Base 4 — Upper bound on s

There is no (129, 259, 2039)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 861104 942134 763004 984117 900301 897919 051149 577044 469980 626682 598239 590941 699924 916323 812513 963484 778061 889012 318604 185293 764946 774842 146480 905363 128186 112630 > 4²⁵⁹ [i]