MinT - Best Known (96, 96+98, s)-Nets in Base 4

Best Known (96, 96+98, s)-Nets in Base 4

(96, 96+98, 104)-Net over F₄ — Constructive and digital

Digital (96, 194, 104)-net over F₄, using

t-expansion [i] based on digital (73, 194, 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]

(96, 96+98, 144)-Net over F₄ — Digital

Digital (96, 194, 144)-net over F₄, using

t-expansion [i] based on digital (91, 194, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(96, 96+98, 1501)-Net in Base 4 — Upper bound on s

There is no (96, 194, 1502)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 645 766353 580978 364307 063509 862756 587322 636700 150897 602440 926900 923853 622872 848857 243397 333505 658126 364396 851934 548806 > 4¹⁹⁴ [i]