MinT - Best Known (90, 255, s)-Nets in Base 4

Best Known (90, 255, s)-Nets in Base 4

(90, 255, 104)-Net over F₄ — Constructive and digital

Digital (90, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 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]

(90, 255, 129)-Net over F₄ — Digital

Digital (90, 255, 129)-net over F₄, using

t-expansion [i] based on digital (81, 255, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(90, 255, 699)-Net in Base 4 — Upper bound on s

There is no (90, 255, 700)-net in base 4, because

1 times m-reduction [i] would yield (90, 254, 700)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 865 098939 183549 315684 549506 600970 545332 167698 913148 311779 962378 002639 046182 534931 714962 061007 252742 063840 065366 243195 027742 873633 308932 771770 050029 698910 > 4²⁵⁴ [i]