MinT - Best Known (195−121, 195, s)-Nets in Base 4

Best Known (195−121, 195, s)-Nets in Base 4

(195−121, 195, 104)-Net over F₄ — Constructive and digital

Digital (74, 195, 104)-net over F₄, using

t-expansion [i] based on digital (73, 195, 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]

(195−121, 195, 112)-Net over F₄ — Digital

Digital (74, 195, 112)-net over F₄, using

t-expansion [i] based on digital (73, 195, 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]

(195−121, 195, 635)-Net in Base 4 — Upper bound on s

There is no (74, 195, 636)-net in base 4, because

1 times m-reduction [i] would yield (74, 194, 636)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 656 730183 008550 685270 130013 541869 595629 995222 575430 500335 750420 212699 697484 997910 314398 832716 844440 880768 135060 213728 > 4¹⁹⁴ [i]