MinT - Best Known (206−131, 206, s)-Nets in Base 4

Best Known (206−131, 206, s)-Nets in Base 4

(206−131, 206, 104)-Net over F₄ — Constructive and digital

Digital (75, 206, 104)-net over F₄, using

t-expansion [i] based on digital (73, 206, 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]

(206−131, 206, 112)-Net over F₄ — Digital

Digital (75, 206, 112)-net over F₄, using

t-expansion [i] based on digital (73, 206, 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]

(206−131, 206, 609)-Net in Base 4 — Upper bound on s

There is no (75, 206, 610)-net in base 4, because

1 times m-reduction [i] would yield (75, 205, 610)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2853 880648 612375 687389 270903 479818 294770 814990 814451 667283 165042 113354 968202 189819 929250 716626 056373 848720 767469 745276 750113 > 4²⁰⁵ [i]