MinT - Best Known (95, 95+153, s)-Nets in Base 4

Best Known (95, 95+153, s)-Nets in Base 4

(95, 95+153, 104)-Net over F₄ — Constructive and digital

Digital (95, 248, 104)-net over F₄, using

t-expansion [i] based on digital (73, 248, 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]

(95, 95+153, 144)-Net over F₄ — Digital

Digital (95, 248, 144)-net over F₄, using

t-expansion [i] based on digital (91, 248, 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]

(95, 95+153, 817)-Net in Base 4 — Upper bound on s

There is no (95, 248, 818)-net in base 4, because

1 times m-reduction [i] would yield (95, 247, 818)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 54422 205347 974388 424861 462987 610564 783303 527059 056307 523001 217134 842895 321249 526185 238159 234012 462426 077715 670167 463589 751379 457983 458612 207139 857200 > 4²⁴⁷ [i]