MinT - Best Known (242−168, 242, s)-Nets in Base 4

Best Known (242−168, 242, s)-Nets in Base 4

(242−168, 242, 104)-Net over F₄ — Constructive and digital

Digital (74, 242, 104)-net over F₄, using

t-expansion [i] based on digital (73, 242, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(242−168, 242, 112)-Net over F₄ — Digital

Digital (74, 242, 112)-net over F₄, using

t-expansion [i] based on digital (73, 242, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(242−168, 242, 513)-Net in Base 4 — Upper bound on s

There is no (74, 242, 514)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 237920 586670 244877 605783 242327 912553 679851 036070 773195 913437 898847 106986 189603 310633 948098 233966 376323 259489 725564 228972 539271 038310 156738 157440 > 4²⁴² [i]